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Logarithms 0001
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  • Logarithms

    0001

  • 1 1 Exponents.................................5

    1 2 Logarithm Form....................168

    1 3 Change Exponent to Logs...351

    1 4 Decimals 2/4 and 3/6............460

    1 5 Decimals 7, 8, 9, and 5.........634

    1 6 Go Backwards......................778

    2 1 Add Logarithms....................884

    2 2 Carry Logarithms................1051

    2 3 Subtract Logarithms..........1215

    2 4 Fraction Logs......................1344

    2 5 Fractions Less Than 1........1499

    2 6 Logs of Decimals................1654

    Log

    Add

    Subtract

    and

    Fractions

    0002

  • 3 1 Logs for 2 Digit Numbers......1774

    3 2 Logs for Scientific Notation..1959

    3 3 Power Logarithms.................2076

    3 4 Radical Logarithms...............2237

    4 1 Other Bases Logarithms.......2403

    4 2 Change to Other Bases.........2497

    4 3 Exponential Equations..........2642

    4 4 Same Base Equations...........2820

    5 1 Log Equations.......................2967

    5 2 Antilogarithms.......................3066

    5 3 Take Log of Both Sides........3231

    Other

    Bases

    and

    Equations

    Equations

    With Logs

    2 Digit

    and

    Power

    Logs

    0003

  • 5 4 Equations With MA Rule....3453

    5 5 Fraction Logarithms..........3641

    6 1 Natural Numbers................3797

    6 2 Continuous Growth Logs..3981

    6 3 Natural Logarithms............4157

    7 1 Earthquakes.......................4360

    7 2 Compare Earthquakes.......4561

    7 3 pH Levels............................4678

    7 4 Sound..................................4862

    Word

    Problems

    Natural

    Logs

    0004

  • 0005

  • 1. What do logarithms find...................62. Exponents with different bases......623. Questions 1..................................1004. Questions 2..................................1205. Performance 1.............................1406. Performance 2.............................154

    Chapter 1 Lesson 1Basic Logarithms

    0006

  • Adjust your screen for correct lettering.

    Chapter 1 Lesson 1

    Basic Logarithms

    What do logarithms find?

    0007

  • Logarithm sounds like a log has rhythm.

    Logarithm

    0008

  • Sorry, no trees playing drums here, although that is funny.

    0009

  • Well, I'm not the one who came up with a crazy name.

    0010

  • True. I don't know who named it, but it's a new way to write numbers.

    What does an exponent do?

    0011

  • 10 2 ExponentBase

    The exponent shows how many times to multiply the base.

    0012

  • Ok, what does it equal?

    10 2 ExponentBase

    0013

  • 10 = 1002

    Cheezy. That equals 100.

    0014

  • 10 = 1002

    Yeah, but what's the name forit? I came up with a name myself.

    0015

  • 10 = 1002

    Real Number

    Why is it called Real Number?

    0016

  • 10 = 1002

    Real Number

    It needed a name, just like base and exponent. It's a real number.

    Lots to do. Time to move on.

    0017

  • So, what do logarithms do?

    Logarithms

    0018

  • Scientific notation is one way of writing numbers.

    Logarithms is another step.

    0019

  • Big step or little step?

    0020

  • Now you can write any number by it's exponent.

    Very Big.

    0021

  • Ummm, you just said that.

    0022

  • True. And that's how big this idea is. I'll explain it.

    0023

  • 10 2

    You know, we already use numbers to write exponents.

    0024

  • Yeah, that's the 1st step to it. I'll write it in bigger words.

    0025

  • I t finds exponents.

    I still have no idea.

    0026

  • Instead of thinking about 100as the number, think of the 2.

    I'll show you what I mean.

    0027

  • You already know 2 is the exponent that makes 100.

    10 = 1002

    0028

  • We've done that like 10 times.

    10 = 1002

    0029

  • So, if I make the exponenta 3, what's the real number?

    10 = ?3

    0030

  • Now the real number is 1000.

    10 = 10003

    0031

  • I'll make a chart to show it.

    The exponent counts the places.

    10 = 10003

    0032

  • 10 100 210 1000 3

    Base Real Number Exponent

    Ok, I see what it makes.

    0033

  • 10 100 210 1000 3

    Base Real Number Exponent

    We'll see. I'll add another one.

    0034

  • 10 100 210 1000 3

    4

    Base Real Number Exponent

    That's all there is? Just 4?

    0035

  • 10 100 210 1000 3

    4

    Base Real Number Exponent

    What real number with base 10 makes it 4?

    0036

  • 10 = 10,0004

    That's 10,000, because there's 4 places.

    0037

  • 10 = 10,0004

    That's how to think of numbers as their exponents. Think about it.

    0038

  • 10 100 210 1000 3

    2 and 3 are the number.

    Base Real Number Exponent

    0039

  • 10 100 210 1000 3

    You do need the base.Here's a problem with it.

    Base Real Number Exponent

    0040

  • 10 x 102

    What's 10 squared x 10 cubed?

    3

    0041

  • 10 x 102

    That's a really old problem. Just use the MA Rule.

    3

    0042

  • 10 x 10 = 102

    Add 2 + 3 is 5, so 10 to the 5th.

    3 5

    0043

  • 10 x 10 = 102

    I'll change the exponents.

    3 5

    0044

  • 10 x 103

    Instead of 2, it's a 3. What does it equal?

    3

    0045

  • 10 x 103

    But, it's a different problem.Another easy one. I know it.

    3

    0046

  • 10 x 10 = 103 3 6

    So, add them.10 to the 6th is 1,000,000.

    0047

  • 10 x 10 = 103 3 6

    So, what changed and what told you what the number was?

    0048

  • 10 x 10 = 103 3 610 x 10 = 102 3 5

    The exponent is what changed.

    0049

  • 10 x 10 = 103 3 610 x 10 = 102 3 5

    That's why it works. Theexponent told you the number.

    0050

  • So, this log thing is going to change everything?

    0051

  • Pretty much true. It will be totally different.

    0052

  • 10 = 1002

    What are the names for the numbers in exponent form?

    Qs

    0053

  • 10 = 1002 Real Number

    Exponent

    Base

    Base to the exponent equals a real number.

    0054

  • What does a logarithm do?

    0055

  • I t finds exponents.

    The exponent is the main number.

    0056

  • 10 2

    What does the exponent on base 10 show you?

    0057

  • 10 = 1002

    2 counts the zeros.

    Place Value

    0058

  • How does changing the exponent change the numbers?

    10 5 10 2

    0059

  • 10 = 100,00051 2 3 4 5

    Change the exponentchanges the real number.

    10 = 10021 2

    (Along with the base.)

    0060

  • 0061

  • Chapter 1 Lesson 1

    Basic Logarithms

    Exponents with different bases.

    0062

  • Does all this use different bases besides 10?

    0063

  • Good question, becausebases is what made it happen.

    I'll go over different bases.

    0064

  • 10 = 10003

    If we change the base to another number then it willmake a different real number.

    I'll change it to a 2.

    0065

  • 2 = 83

    Wow! Big difference.

    0066

  • 2 = 83

    Same exponent, but the base number gives a different answer.

    Here's a different one.

    0067

  • 5 = 252

    You know 5 squared is 25.

    What happens when you change the exponent to a 3?

    0068

  • 5 = 1253

    Changing the exponent really changes the real number.

    0069

  • 5 = 1253

    There is a word for that.

    0070

  • Exponential

    Duh. It's got the word exponent in it.

    0071

  • If you have a stock worth Rs 25one day and it's Rs 125 the next...

    0072

  • 5 = 1253

    That would be alot of money.

    0073

  • 5 = 1253

    I don't think you get it. The next morning you wake up and...

    0074

  • 5 = 6254

    Rs 625?! Yeah, I would love that.

    0075

  • Remember, this is algebra.

    The pow er of exponents.

    0076

  • What do you mean,"algebra"? I thought it was algebra 2.

    0077

  • Algebra in general. Thatmeans we need variables.

    I'll make 1 so you can see it.

    0078

  • 2 = x3

    Wow. That is a tough problem. Not really.

    0079

  • 2 = x3

    Take your time. How do you solve it?

    0080

  • 2 = x 8 = x

    3

    Duh, 2 x 2 x 2 equals 8.

    0081

  • Very good. I'll change the exponent.

    0082

  • 2 = x3.7

    I was kidding last time. This is a tough problem.

    0083

  • 2 = 133.7

    Logarithms can solve that. I'll move the variable.

    0084

  • 2 = 16x

    Now X is the exponent.

    0085

  • 2 = 16x

    How do you solve for X?

    0086

  • 2 = 16x

    Does it count if I know the answer?

    0087

  • 2 = 16x

    Alittle. What is the answer?

    0088

  • 2 = 164

    X is 4, because 2 x 2 is 4 and 4 x 4 is 16.

    0089

  • I'll change it alittle.

    Here's another problem.

    0090

  • 10 = 20x

    Nope. Don't know that one either

    0091

  • 10 = 201.3

    Again. Logarithms will solve that.

    0092

  • Logarithms

    I'm guessing that logarithms is alot tougher than I thought.

    0093

  • I guarantee that you willlearn more about exponents.

    0094

  • Is that a money back guarantee?

    0095

  • Sure, if I had any. Trust me. You will learn exponents.

    0096

  • Qs

    10 2

    Why is the base important?

    5 2

    0097

  • 5 = 252

    Different base numbers make a different real number.

    10 = 1002

    0098

  • 0099

  • Practice #1

    Chapter 1 Lesson 1

    Basic Logarithms

    How logarithms use exponents.

    0100

  • What are the names for the numbers in exponent form?

    10 = 100212 3

    0101

  • 10 = 1002Base

    Exponent

    Real Number

    Base to the exponent equals the real number.

    0102

  • What does a logarithm do?

    0103

  • I t finds exponents.

    The exponent is the main number.

    0104

  • How does changing the exponent change the numbers?

    10 5 10 2

    0105

  • 10 = 100,00051 2 3 4 5

    Change the exponentchanges the real number.

    10 = 10021 2

    (Along with the base.)

    0106

  • 10 2

    What does the exponent 2 on base 10 show you?

    0107

  • 10 = 1002

    2 counts the zeros

    0108

  • 10 = 1000x

    What exponent solves base 10 equals 1000?

    Problems

    0109

  • 10 = 10003

    It's 3. 10 to the 3rd is 1000.

    0110

  • What exponent solves base 10 equals 1 million?

    10 = 1,000,000x

    0111

  • 10 = 1,000,0006

    6 because there's 6 places in 1,000,000.

    0112

  • 10 = ?4

    10 to the 4th makes what number?

    0113

  • 10 = 10,0004

    10 to the 4th is 10 thousand.

    0114

  • 2 = ?4

    What are 2 to the 4th and 6th?

    2 = ?6

    0115

  • 2 = 164

    2 to the 4th is 16 and 2 to the 6th is 64.

    2 = 646

    0116

  • 5 = ?2

    What is 5 squared and cubed?

    5 = ?3

    0117

  • 5 = 252

    5 squared is 25 and 5 to the 3rd is 125.

    5 = 1253

    0118

  • 0119

  • Practice #2

    Chapter 1 Lesson 1

    Basic Logarithms

    How logarithms use exponents.

    0120

  • What are the names for the numbers in exponent form?

    10 = 100212 3

    0121

  • 10 = 1002Base

    Exponent

    Real Number

    Base to the exponent equals the real number.

    0122

  • What does a logarithm do?

    0123

  • I t finds exponents.

    The exponent is the main number.

    0124

  • How does changing the exponent change the numbers?

    10 5 10 2

    0125

  • 10 = 100,00051 2 3 4 5

    Change the exponentchanges the real number.

    10 = 10021 2

    (Along with the base.)

    0126

  • What does the exponent 2 on base 10 show you?

    10 2

    0127

  • 10 = 1002

    2 counts the zeros

    0128

  • 10 = 100x

    What exponent solves base 10 equals 100?

    Problems

    0129

  • 10 = 1002

    It's 2. 10 squared is 1000.

    0130

  • What exponent solves base 10 equals 10 million?

    10 = 10,000,000x

    0131

  • 10 = 10,000,0007

    7 because there's 7 places in 10 million.

    0132

  • 10 = ?5

    10 to the 5th makes what number?

    0133

  • 10 = 100,0005

    10 to the 5th is 100 thousand.

    0134

  • 3 = ?3

    What are 3 cubed and to the 4th?

    3 = ?4

    0135

  • 3 = 273 3 = 814

    3 cubed is 27and 3 to the 4th is 81.

    0136

  • 2 = ?3

    What is 2 cubed and 2 to the 4th?

    2 = ?4

    0137

  • 2 = 83 2 = 164

    2 cubed is 8 and to the 4th is 16.

    0138

  • 0139

  • Performance #1

    Chapter 1 Lesson 1

    Basic Logarithms

    How logarithms use exponents.

    0140

  • 10 = 1000x

    Find the exponents.

    10 = 10,000x

    0141

  • 10 = 1000

    10 = 10,0004

    3

    1000 is cubed and 10,000 is 4th.

    0142

  • 10 = 1,000,000x

    Find the exponents.

    10 = 10,000,000x

    0143

  • 10 = 1,000,0006

    10 to the 6th is 1 million and10 to the 7th is 10 million.

    10 = 10,000,0007

    0144

  • 10 = x9

    10 = x10

    What is 10 to the 9th and 10th?

    0145

  • 1,000,000,000

    10,000,000,000

    10 = 9

    10 = 10

    0146

  • 10 = x1

    10 = x0

    What is 10 to the 1st and 0 power?

    0147

  • 10 = 101

    10 = 10

    10 to the 1st is 10 and any number to the 0 power is 1.

    0148

  • 2 = ?4

    What are 2 to the 4th and 6th?

    2 = ?6

    0149

  • 2 = 164

    2 to the 4th is 16 and 2 to the 6th is 64.

    2 = 646

    0150

  • 5 = ?3

    What are 5 to the 3rd and 4th?

    5 = ?4

    0151

  • 5 = 1253 5 = 6254

    5 to the 3rd is 125 and 5 to the 4th is 625.

    0152

  • 0153

  • Performance #2

    Chapter 1 Lesson 1

    Basic Logarithms

    How logarithms use exponents.

    0154

  • 10 = 100x

    Find the exponents.

    10 = 100,000x

    0155

  • 10 = 100

    10 = 100,0005

    2

    100 is squared and 100,000 is 5th.

    0156

  • 10 = 100,000,000x

    Find the exponents.

    10 = 1,000,000,000x

    0157

  • 10 = 100,000,000

    10 = 1,000,000,000

    8

    10 to the 8th is 100 million and10 to the 9th is 1 billion.

    9

    0158

  • 10 = x10

    10 = x11

    What is 10 to the 10th and 11th?

    0159

  • 10,000,000,000

    100,000,000,000

    10 = 10

    10 = 11

    10 to the 10th is 10 billion and10 to the 11th is 100 billion.

    0160

  • 10 = x3

    10 = x0

    What is 10 to the 3rd and 0 power?

    0161

  • 10 = 10003

    10 = 10

    10 to the 3rd is 1000 and any number to the 0 power is 1.

    0162

  • 2 = ?3

    What are 2 to the 3rd and 5th?

    2 = ?5

    0163

  • 2 = ?3 2 = ?5

    2 to the 3rd is 8 and 2 to the 5th is 32.

    0164

  • 3 = ?3

    What are 3 to the 3rd and 4th?

    3 = ?4

    0165

  • 3 = 273 3 = 814

    3 to the 3rd is 27 and 3 to the 4th is 81.

    0166

  • 0167

  • 1. What do logarithms look like?..1682. How to say a logarithm............2273. Questions 1.............................2834. Questions 2.............................3055. Performance 1........................3236. Performance 2........................337

    Chapter 1 Lesson 2Basic Logarithms

    0168

  • Adjust your screen for correct lettering.

    Chapter 1 Lesson 2

    Basic Logarithms

    What do logarithms look like?

    0169

  • So, when do I get to see what a logarithm looks like?

    0170

  • Your wish is my command. I'll show you the left side.

    0171

  • log 100 10

    Does log mean logarithm?

    0172

  • log 100 10

    Yup. The base is a little number and the real number is next to it.

    Watch where the exponent goes.

    base

    real number

    0173

  • log 100 = 210

    It equals the exponent?

    Exponent

    0174

  • log 100 = 210

    The exponent is what's important. Where is the base number at?

    Exponent

    0175

  • log 100 = 210

    Base is the little number under it.

    Base

    0176

  • log 100 = 210

    Right. Where does it go to get the exponent?

    Base

    0177

  • log 100 = 210

    Up the slide. That's 10 squared.

    0178

  • log 100 = 210

    Where is the real number at?

    0179

  • log 100 = 210

    Go across to the real number.

    0180

  • log 100 = 210

    That's the logarithm form.What number does it look like?

    0181

  • log 100 = 210

    It looks like the number 7 .

    7

    0182

  • log 100 = 210

    7 shows how it works. I'll get another problem.

    0183

  • log 1000 10

    Alot like the last one.

    0184

  • log 100010

    Ok, what's the exponent here?

    0185

  • log 1000 = 310

    How did you know that?

    0186

  • log 1000 = 310

    I'll show you how to count place values.

    0187

  • 1 , 0 0 01 2 3

    Count the places to the 1st digit.

    0188

  • So, the exponent is 3?

    1 , 0 0 01 2 3

    Ok, I get how that works.

    0189

  • log 1000 = 310

    Yes. Where does it start to find the exponent form?

    0190

  • log 1000 = 310

    Start at the base 10 and slide upto the 3.

    0191

  • log 1000 = 310

    Where does it go from there?

    0192

  • log 1000 = 310

    Go across to finish the 7.

    0193

  • log 1000 = 310

    So, what's the exponent form?

    0194

  • 10 to the 3rd makes 1000.

    10 10003 =

    0195

  • 10 10003

    10 to the 3rd power is 1000.

    =

    log 1000 = 310

    0196

  • 10 = 10,000?

    Think about how you get the exponent for 10,000, base 10.

    0197

  • 1 0 , 0 0 01 2 3 4

    Count the places to after the 1st digit.

    0198

  • 1 0 , 0 0 01 2 3 4

    So, what's the exponent?

    0199

  • 10 = 10,0004

    Easy enough. It's 4.Make a chart for it.

    0200

  • log 10 = 1log 100 = 2log 1000 = 3log 10,000 = 4

    The exponent shows the place value part to the real number.

    0201

  • 1 x 10 5

    When you look at scientificnotation, it's the exponent on 10.

    That's how scientific notation is alot like logarithms. What's this one?

    0202

  • 1 0 0 ,0 0 01 2 3 4 5

    10

    So, the exponent would be 5.

    is5

    0203

  • 1 0 0 ,0 0 01 2 3 4 5

    10is 5

    Good!! I'll go over a few to see if you make exponent form.

    0204

  • log 10 = x10

    One very nice logarithm.What's the exponent here?

    0205

  • log 10 = x10

    10 has just 1 zero, so it's a 1.

    0206

  • log 10 = 110

    Right. What's the exponent form?

    0207

  • log 10 = 110

    First, start at the base. I'll show you.

    0208

  • log 10 = 110

    Upto the exponent and across to the real number.

    0209

  • log 10 = 110

    What's the exponent form?

    0210

  • log 10 = 110

    The exponent is 10 to the 1st.

    10 = 101

    0211

  • log 10 = 110

    That's what you think about.Exponent form starts at the base.

    10 = 101

    One more...

    0212

  • log 1 ,000,000 = 610

    Last one.What's the exponent form?

    0213

  • log 1 ,000,000 = 610

    It's six. Ok, I think I see it now.

    0214

  • log 1 ,000,000 = 610

    10 to the 6th is 1 million.

    10 = 1,000,0006

    0215

  • The next lesson is important.

    0216

  • Qs

    log 100 = ?10

    What do logarithms equal?

    0217

  • log 100 = 210

    Logs equal the exponent.

    0218

  • Where is the base in a logarithm?

    log 100 = 210

    0219

  • log 100 = 210

    Base

    Base is the lit t le number.We don't always write it if it's 10.

    0220

  • Where does it start to change log to exponent form?

    log 100 = 210

    0221

  • What shape shows how to change it?

    log 100 = 210

    Start at the base number.

    0222

  • 10 squared is 100.

    log 100 = 210

    Think of a 7 .

    0223

  • log x = 310

    If we change the log exponent to a 3, what does it change?

    0224

  • log 1000 = 310

    Real Number is 1000. Change the exponent changes the real number.

    0225

  • 0226

  • Chapter 1 Lesson 2

    Basic Logarithms

    How to say a logarithm.

    0227

  • Before we go any further, I need to go over how to say them.

    Say a logarithm.

    0228

  • How to say them? That's too easy.

    0229

  • log 100 = 210

    Ok, how do you say this log?

    0230

  • log 100 = 210

    Ummm, probably log of something something something.

    0231

  • Say Logarithm of 100, base 10, is 2.

    log 100 = 210

    Just look for the checkmark.

    0232

  • log 100 = 210

    What checkmark is that?

    0233

  • That starts the checkmark.

    log 100 = 210

    Start with Log of 100.

    0234

  • log 100 = 210

    Go to Base 10. That's the bottom of the checkmark.

    0235

  • The log exponent is the end of the checkmark.

    log 100 = 210

    Finish at is 2 .

    I'll change the problem.

    0236

  • log 10 = 110

    How do you say this one?

    0237

  • log 10 = 110

    Can you show me the checkmark?

    0238

  • log 10 = 110

    Remember where it starts.

    0239

  • log 10 = 110

    I know the 1st part is Log of 10.Ok, here it is...

    0240

  • It's Logarithm of 10 base 10 is 1.

    log 10 = 110

    0241

  • I've got one more.

    Work on the middle part.

    0242

  • log 1000 = 310

    Start with log of 1000.

    Here's the rest.

    0243

  • It's Logarithm of 1000 base 10 is 3.

    10log 1000 = 3

    I know this one.

    0244

  • I'll make initials for it so you can remember it.

    0245

  • What does that tell me?

    RBE

    0246

  • Real number to the base to the exponent or...

    0247

  • I think I'll use the checkmark.

    Checkmark

    0248

  • At least you know how to say it now.

    0249

  • I know logarithms are important, but do we really use it for anything?

    0250

  • Good point. No use learning something we'll never use.

    0251

  • How about earthquakes? Are they important?

    0252

  • Great day!! They destroy buildings and everything.

    0253

  • They use logarithms.How about how loud a sound is?

    0254

  • I know. You're going to tellme they use logarithms, too.

    0255

  • Both earthquakes and sounduse logarithms to measure them.

    Sound

    0256

  • Anything else I might need?

    0257

  • Is that like the PH on phone?

    PH Levels

    0258

  • It's how acid or basesomething is. It uses logs.

    Say each one, P, then H.

    0259

  • Don't tell me the Rule of 3s uses logarithms too?

    Rule of 3s

    0260

  • The opposite way around.Logarithms use the Rule of 3s.

    0261

  • How do logarithms do that?

    0262

  • Relax. This makes it easier to figure out. I'll show you.

    0263

  • What's this real number?

    log ? = 6

    0264

  • log 1,000,000 = 6

    Log of a million is 6.

    Am I right?

    0265

  • log 1,000,000 = 6

    Uhhh, you forgot the base 10 part.

    0266

  • log 1,000,000 = 6

    You didn't write it in there,so I figured it wasn't important.

    0267

  • log 1,000,000 = 6

    We use base 10 so muchthat you don't have to write it, but you still have to say it.

    0268

  • log 1,000,000 = 6

    Hey, less writing for me.

    0269

  • log 1,000,000 = 6

    There's 6 places in millions. That's the Rule of 3s.

    0270

  • log 1,000,000 = 6

    Ok, I'll make the next one.

    0271

  • log ? = 7

    That would add 1 more. All the 10s use it.

    I've got that together.

    0272

  • log 10,000,000 = 7

    6 places in million's place,so add 1 more to get 10s.

    1 more thing to show you.

    0273

  • 2 = log 10010

    Hey, it's backwards.

    0274

  • Some books write the logarithm backwards.

    2 = log 10010

    Same stuff. Nothing changes.

    0275

  • Qs

    log 100 = 2 10

    Where do you start to say a log?

    0276

  • log 100 = 210

    Start with Log of 100.

    0277

  • log 100 = 210

    What shape does saying a log use?

    0278

  • log 100 = 210

    Checkmark

    Say Logarithm of 100, base 10, is 2.

    0279

  • log 10,000 = 410

    How do you say this logarithm?

    0280

  • log 10,000 = 410

    Say Logarithm of 10,000, base 10, is 4.

    Start at log 10,000.

    0281

  • 0282

  • Practice #1

    Chapter 1 Lesson 2

    Basic Logarithms

    Name 3 parts to logarithms and how to say them.

    0283

  • What do logarithms equal?

    log 100 = ?10

    0284

  • log 100 = 210

    ExponentReal Number

    Logarithms equal the exponent. Where is the base in a logarithm?

    0285

  • log 100 = 210

    Base

    Base is the lit t le number.We don't always write it if it's 10.

    0286

  • Where does it start to change log to exponent form?

    log 100 = 210

    0287

  • What shape shows how to change it?

    log 100 = 210

    Start at the base number.

    0288

  • 10 squared is 100.

    log 100 = 210

    Think of a 7 .

    0289

  • log x = 310

    If we change the log exponent to a 3, what does it change?

    0290

  • log 1000 = 310

    Real Number is 1000. Change the exponent changes the real number.

    0291

  • Problems

    log 10,000 = x10

    How does log of 10,000, base 10, show you the exponent?

    0292

  • log 10,000 = x10

    How does it make the exponent?

    Look at the real number.

    0293

  • log 10,000 = 410

    So the log exponent is 4.

    I t has 4 zeros.

    0294

  • log 1000 = 310

    What's the 1st step to change log to exponent form?

    0295

  • 10 3

    log 1000 = 310

    10 cubed pow er.Start at the base.

    How do you finish it?

    0296

  • 10 = 1,0003

    log 1000 = 410

    10 to the 3rd power is 1,000.

    Go across to the real number.

    0297

  • log 100,000,000 = x10

    What is the log exponentfor log of 100 million, base 10?

    0298

  • log 100,000,000 = 810

    What is the exponent form?

    Log of 100 million, base 10, is 8 .

    0299

  • 10 = 100,000,0008

    log 100,000,000 = 810

    10 to the 8th is 100 million.

    0300

  • log x = 610

    What is the real number for base 10 to the 6th?

    0301

  • What is the exponent form?

    Logarithm of 1 ,000,000, base 10, is 6 .

    log 1 ,000,000 = 610

    0302

  • 10 = 1,000,0006

    log 1,000,000 = 610

    10 to the 6th is 1 million.

    0303

  • 0304

  • Practice #2

    Chapter 1 Lesson 2

    Basic Logarithms

    Name 3 parts to logarithms and how to say them.

    0305

  • Qs

    log 100 = 2 10

    Where do you start to say a log?

    0306

  • log 100 = 210

    Start with Log of 100.

    0307

  • log 100 = 210

    What shape does saying a log use?

    0308

  • log 100 = 210

    Checkmark

    Say Logarithm of 100, base 10, is 2.

    0309

  • Problems

    log 100,000 = x10

    How does log of 100,000, base 10, show you the exponent?

    0310

  • log 100,000 = x10

    How does it make the exponent?

    Look at the real number.

    0311

  • log 100,000 = 510

    So the log exponent is 5.

    I t has 5 zeros.

    0312

  • log 100 = 210

    What's the 1st step to change log to exponent form?

    0313

  • 10 2

    log 100 = 210

    10 squared.Start at the base.

    How do you finish it?

    0314

  • 10 = 1002

    log 100 = 310

    10 squared is 100.

    Go across to the real number.

    0315

  • log 1,000,000,000 = x10

    What is the log exponentfor log of 1 billion, base 10?

    0316

  • log 1,000,000,000 = 910

    What is the exponent form?

    Log of 1 billion, base 10, is 9 .

    0317

  • 10 = 1,000,000,0009

    log 1,000,000,000 = 910

    10 to the 9th is 1 billion.

    0318

  • log x = 710

    What is the real number for base 10 to the 7th?

    0319

  • What is the exponent form?

    Logarithm of 10 million base 10, is 7 .

    log 10,000,000 = 710

    0320

  • 10 = 10,000,0007

    log 10,000,000 = 710

    10 to the 7th is 10 million.

    0321

  • 0322

  • Performance #1

    Chapter 1 Lesson 2

    Basic Logarithms

    Name 3 parts to logarithms and how to say them.

    0323

  • log 10,000 = x10

    What exponent goes with each logarithm?

    log 100,000 = x10

    0324

  • log 10,000 = 410

    log 100,000 = 510

    10,000 is 4 and 100,000 is 5.

    0325

  • log 10 = x10

    What exponent goes with each logarithm?

    log 1 = x10

    0326

  • 10 is 1 and 1 is 0.

    log 10 = 110

    log 1 = 010

    0327

  • Find the real numbers.

    log x = 5

    log x = 4

    0328

  • log 100,000 = 5

    log 10,000 = 4

    5 is 100 thousand and 4 is 10 thousand.

    0329

  • Find the real numbers.

    log x = 6

    log x = 8

    0330

  • 6 is 1 million and 8 is 100 million.

    log 1,000,000 = 6

    log 100,000,000 = 8

    0331

  • log 10,000 = 410

    Change this log to exponent form.

    0332

  • 10 10,0004 =

    log 10,000 = 410

    10 to the 4th is 10,000.

    0333

  • Change this log to exponent form.

    log 100 = 210

    0334

  • 10 squared is 100.

    10 1002 =

    log 100 = 210

    0335

  • 0336

  • Performance #2

    Chapter 1 Lesson 2

    Basic Logarithms

    Name 3 parts to logarithms and how to say them.

    0337

  • log 1 ,000 = x10

    What exponent goes with each logarithm?

    log 1 ,000,000 = x10

    0338

  • log 1,000 = 310

    log 1,000,000 = 610

    1,000 is 3 and 1,000,000 is 6.

    0339

  • log 100 = x10

    What exponent goes with each logarithm?

    log 1 = x10

    0340

  • 100 is 2 and 1 is 0.

    log 100 = 210

    log 1 = 010

    0341

  • Find the real numbers.

    log x = 3

    log x = 2

    0342

  • log 1,000 = 3

    log 100 = 2

    3 is 1000 thousand and 2 is 100.

    0343

  • Find the real numbers.

    log x = 7

    log x = 9

    0344

  • 7 is 10 million and 0 is 1 billion.

    log 10,000,000 = 7

    log 1,000,000,000 = 9

    0345

  • log 1 ,000 = 310

    Change this log to exponent form.

    0346

  • 10 10003 =

    log 1000 = 310

    10 to the 3rd is 1000.

    0347

  • Change this log to exponent form.

    log 10 = 110

    0348

  • 10 to the first is 10.

    10 101 =

    log 10 = 110

    0349

  • 0350

  • 1. Change Exponents to Logs..3512.3. Questions 1..........................3944. Questions 2..........................4135. Performance 1.....................4326. Performance 2.....................446

    Chapter 1 Lesson 3Basic Logarithms

    0351

  • Chapter 1 Lesson 3

    Basic Logarithms

    Change Exponent form to Logarithm form

    0352

  • I keep on thinking about going camping.

    0353

  • Camping? Because you use logs to make a fire?

    0354

  • I'm glad you thought of it.Think of it, real logs this time.

    0355

  • Oh, yeah. It would probablyrain and we'd sit by a lighter.

    0356

  • Well, think about it.I'm an expert at real logs.

    0357

  • I'm an expert at calling forpizza. Well, more stuff to do.

    0358

  • log 100 = 210

    What did we use to get exponent form?

    0359

  • log 100 = 210

    The number 7. I'll show you.

    0360

  • log 100 = 210

    Base to exponent across to real number.

    0361

  • log 100 = 210

    I'm impressed. Time for the next step.

    0362

  • 10 = 1,0003

    So, what are we doing now?

    0363

  • 10 = 1,0003

    You know how to go from logto exponent. We'll go backwards.

    0364

  • Total, 100%, turbo brain power.

    How do you change an exponent to logarithm form?

    0365

  • 10 = 1,0003

    This figure is kind of like the 7. You can follow it to make a log.

    0366

  • 10 = 1,0003

    What does it make, a pretzel?

    0367

  • 10 = 1,0003

    It's an .

    (That's a 7 turned upside down.)

    L

    0368

  • 10 = 1,0003

    Where does it start?It can't start at the base number.

    0369

  • 10 = 1,0003

    Nope, it starts at the other end.

    0370

  • 10 = 1,0003

    Say logarithm of 1000.

    Watch where it goes.

    Use the Real Number.

    0371

  • 10 = 1,0003

    Logarithm of 1000, Base 10 .

    Last step?

    Next, go across.

    0372

  • 10 = 1,0003

    Finish the L.Log of 1000, base 10, is 3.

    log 1 ,000 = 310

    0373

  • 10 10,0004

    Where does it start?

    Change this exponent to log form.

    =

    0374

  • 10 10,0004 =

    Start at logarithm of 10,000.

    log 10,000

    0375

  • 10 10,0004 =

    Then across to base 10. Here it is...

    log 10,00010

    0376

  • 10 10,0004 =

    log 10,000 = 410

    Log of 10,000, base 10 is 4.

    0377

  • 10 = 100,0005

    Change this exponent to log form.

    All in 1 step.

    0378

  • log 100,000 = 510

    Start at Log of 100,000, then base 10 is 5.

    10 = 100,0005

    0379

  • 2 = 8x

    We'll do more of this later, but what would this exponent be?

    0380

  • 2 = 8x

    I know 2 x 2 x 2 is 8.

    0381

  • 2 = 83

    Right, 2 cubed is 8.So, what's the log form?

    0382

  • 2 = 83

    Ok, start at 8 and go across.

    0383

  • 2 83 =

    log 8 = 32

    That's log of 8, base 2, is 3.

    0384

  • That's the idea. Any questions?

    0385

  • Logs

    You know, anytime you want to work with real logs, let me know.

    0386

  • Next time I see your dad I'll tellhim to let you cut some wood up.

    0387

  • Qs

    Where do you start to change log into exponent form?

    10 = 1002

    0388

  • Start w ith the real number.

    10 = 1002

    What shape shows the logarithm?

    0389

  • 10 = 1002

    Real number to the base, then up to the exponent.

    Use the L.

    0390

  • 4 = 16?

    Change to a log.What's this exponent?

    0391

  • 4 162 =

    log 16 = 24

    Log of 16, base 2, is 4.

    0392

  • 0393

  • Practice #1

    Chapter 1 Lesson 3

    Basic Logarithms

    Change Exponent form to Logarithm form

    0394

  • Where do you start to change a log into exponent form?

    10 = 1002

    0395

  • Start w ith the real number.

    10 = 1002

    What shape shows the logarithm?

    0396

  • 10 = 1002

    Real number to the base, then up to the exponent.

    Use the L.

    0397

  • 4 = 16?

    Change to a log.What's this exponent?

    0398

  • 4 162 =

    log 16 = 24

    Log of 16, base 2, is 4.

    0399

  • 10 = 1002

    Where do you start to get alog from an exponent equation?

    Problems

    0400

  • 10 = 1002

    Where does it go from there?

    Start at the real number. log 100

    0401

  • 10 = 1002

    What is the last step?

    Across tothe base. log 10010

    0402

  • 10 = 1002

    It follows an L shape.

    Upto theexponent. log 100 = 210

    0403

  • Find the exponent, then find the logarithm form.

    10 = 10,000x

    0404

  • 10 = 10,0004

    log 10,000 = 410log of 10,000, base 10, is 4.

    0405

  • Find the exponent, then find the logarithm form.

    10 = 1,000,000x

    0406

  • 10 = 1,000,0006

    log 1 ,000,000 = 610log of 1,000,000, base 10, is 6.

    0407

  • What's the log form for 27, base 3?

    3 = 27x

    0408

  • 3 = 273

    log 27 = 33log of 27, base 3, is 3.

    0409

  • What's the log form for 16, base 2?

    2 = 16x

    0410

  • 2 = 164

    log 16 = 42log of 16, base 2, is 4.

    0411

  • 0412

  • Practice #2

    Chapter 1 Lesson 3

    Basic Logarithms

    Change Exponent form to Logarithm form

    0413

  • Where do you start to change log into exponent form?

    10 = 1002

    0414

  • Start w ith the real number.

    10 = 1002

    What shape shows the logarithm?

    0415

  • 10 = 1002

    Real number to the base, then up to the exponent.

    Use the L.

    0416

  • 4 = 16?

    Change to a log.What's this exponent?

    0417

  • 4 162 =

    log 16 = 24

    Log of 16, base 2, is 4.

    0418

  • 10 = 10003

    Where do you start to get alog from an exponent equation?

    Problems

    0419

  • 10 = 10003

    Where does it go from there?

    Start at the real number. log 1000

    0420

  • 10 = 10003

    What is the last step?

    Across tothe base. log 100010

    0421

  • 10 = 10003

    It follows an L shape.

    Upto theexponent. log 1000 = 310

    0422

  • Find the exponent, then find the logarithm form.

    10 = 100,000x

    0423

  • 10 = 100,0005

    log 100,000 = 510log of 100,000, base 10, is 5.

    0424

  • Find the exponent, then find the logarithm form.

    10 = 10,000,000x

    0425

  • 10 = 10,000,0007

    log 10,000,000 = 710log of 10,000,000, base 10, is 7.

    0426

  • What's the log form for 125, base 5?

    5 = 125x

    0427

  • 5 = 1253

    log 125 = 35

    log of 125, base 5, is 3.

    0428

  • What's the log form for 64, base 2?

    2 = 64x

    0429

  • 2 = 646

    log 64 = 62log of 64, base 2, is 6.

    0430

  • 0431

  • Performance #1

    Chapter 1 Lesson 3

    Basic Logarithms

    Change Exponent form to Logarithm form

    0432

  • Change this exponent to logarithm form.

    10 = 1,0003

    0433

  • log 1000 = 310

    Log of 1000, base 10 is 3.

    10 = 1,0003

    0434

  • What's the logarithm form?

    10 = 1002

    0435

  • log 100 = 210

    Log of 100, base 10 is 2.

    10 = 1002

    0436

  • Solve it and change to log form.

    10 = x6

    0437

  • log 1 ,000,000 = 610

    Log of 1 million, base 10 is 6.

    0438

  • Solve it and change to log form.

    10 = x8

    0439

  • log 100,000,000 = 8

    Log of 100 million, base 10 is 8.

    0440

  • What's the log form for 64, base 4?

    4 = 64x

    0441

  • 4 = 643

    log 64 = 34log of 64, base 4, is 3.

    0442

  • What's the log form for 625, base 5?

    5 = 625x

    0443

  • 5 = 6254

    log 625 = 45

    log of 625, base 5, is 4.

    0444

  • 0445

  • Performance #2

    Chapter 1 Lesson 3

    Basic Logarithms

    Change Exponent form to Logarithm form

    0446

  • Change this exponent to logarithm form.

    10 = 10,0004

    0447

  • log 10,000 = 410

    Log of 10,000, base 10 is 4.

    10 = 10,0004

    0448

  • What's the logarithm form?

    10 = 101

    0449

  • log 10 = 110

    Log of 10, base 10 is 1.

    10 = 101

    0450

  • Solve it and change to log form.

    10 = x5

    0451

  • log 100,000 = 510

    Log of 100,000 base 10 is 5.

    0452

  • Solve it and change to log form.

    10 = x7

    0453

  • log 10,000,000 = 7

    Log of 10 million, base 10 is 7.

    0454

  • What's the log form for 64, base 2?

    2 = 64x

    0455

  • 2 = 646

    log 64 = 62log of 64, base 2, is 6.

    0456

  • What's the log form for 81, base 3?

    3 = 81x

    0457

  • 3 = 814

    log 81 = 43

    log of 81, base 3, is 4.

    0458

  • 0459

  • 1. Find the log for 2 and 4.......4602. Find the log for 3 and 6.......5213. Questions 1.........................5664. Questions 2.........................5865. Performance 1.....................6066. Performance 2.....................620

    Chapter 1 Lesson 4Basic Logarithms

    0460

  • Chapter 1 Lesson 4

    Basic Logarithms

    Find the log exponent for numbers beginning with 2 and 4.

    0461

  • I hate to say it. I'm sickof numbers that begin with 1.

    0462

  • I have the cure. 2s

    You will love doing this part.

    0463

  • 2s

    2s? That's it?I thought we'd do 2 through 9.

    0464

  • We will, but you have to understand how exponents make numbers.

    Here's the 1st problem.

    0465

  • You know the place value part of this number.

    log 20

    0466

  • Sure, 20 has 1 place after the 1st digit.

    log 20

    0467

  • 1 . ?place value decimal part

    There's the place value part for 20. That's 1 place.

    Guess what's next?

    0468

  • What's the rest of it?

    Decimal for 2?

    0469

  • 1 . ?place value decimal part

    Decimal PartThat's where you find the log exponent for 2. Watch.

    0470

  • 1 . 30place value decimal part

    Decimal PartThe log exponent is 1.30. Any questions?

    0471

  • Lost. Already. Not alittle lost. 100% lost.

    0472

  • I knew that. Let's go back to exponent form.

    0473

  • You know that 10 to the 1st power equals 10.

    10 = 101

    0474

  • Yeah, it has 1 zero.

    10 = 101

    0475

  • 10 = 2?

    What happens whenwe find the exponent for 2?

    0476

  • 10 = 2?

    Well, it's less than 1.

    0477

  • Right. It's the decimal 0.30.

    10 20.30

    We could write 0.3010 , but 100ths are easier to work with.

    =

    0478

  • 10 20.30

    =

    OK, I see that, but how does that work with logarithms?

    0479

  • log 2 = 0.30

    The log exponent for 2 is 0.30.

    0480

  • log 2 = 0.30

    What does the squiggly line mean?

    0481

  • log 2 = 0.30

    It's not an exact answer. We rounded it.

    0482

  • log 2 = 0.30

    Ok, show me another one.

    0483

  • log 20 = ?.30

    If it's the log of 20, how does the log exponent change?

    0484

  • log 20 = ?.30

    It changes the place value part.

    0485

  • log 20 = 1.30

    Right. Now it's log 20, base 10, 1.30.

    0486

  • log 20 = 1.30

    Make an even bigger one.

    0487

  • log 2000 = ?

    So, what's the exponent for 2000?

    0488

  • log 2000 = ?

    3 places and the exponent for 2 is 0.30. I think I got this.

    0489

  • log 2000 = 3.30

    Right. Place value and decimal.

    I do have a memory trick you can use for this.

    3 places

    0490

  • log 2 = 0.30

    See log of 2, remember the 3.

    0491

  • Ok. What's the next number?

    log 2 = 0.30≅

    Oh, because it's 2 then 3.

    0492

  • log 4 = ? realnumber

    logarithm exponent

    You can use log of 2 to find 4.

    0493

  • log 4 = ? realnumber

    logarithm exponent

    How are you going to do that?

    0494

  • log 4 = ? realnumber

    logarithm exponent

    What 's 2 + 2?

    0495

  • log 4 = ? realnumber

    logarithm exponent

    4, why does that matter?

    4

    0496

  • log 4 = 0.60

    Another memory trick.0.30 + 0.30 equals log 4.

    Ok, what's the log of 4?

    0497

  • log 4 = 0.60≅

    Sweet! Just double 0.30.

    0 .30 + 0.30 = 0.60What's the problem?

    0498

  • 4,000

    What's the 1st step to find a log exponent?

    0499

  • 3. ?3 Places in 4,000

    Find place value. It's 3 places.

    Ok, the decimal for 4 is next.

    0500

  • 3. ?3 Places in 4,000

    You're right. What's the decimal for 4?

    0501

  • 3.603 Placesin 4,000

    The first digit, 4.

    Double 0.30 is 0.60.

    0502

  • 3.603 Placesin 4,000

    The first digit, 4.

    I'll put it altogether.

    0503

  • log 4000 = 3.60 realnumber

    logarithm exponent

    Here's logarithm form.

    Tell me the exponent form.

    0504

  • 10 = 4 ,0003.6

    10 to the 3.6 power is 4000. Are we done yet?

    0505

  • Just one more log problem. What should it be?

    0506

  • log 400

    What's the log exponent for 400?

    0507

  • log 400 = 2.60

    That's weird how 2 + 2 works with log exponents.

    Log of 400, base 10, is 2.60.

    0508

  • It makes sense in an exponent way.

    0509

  • So, when are we doingall the other numbers?

    0510

  • We did 2 and 4. The next 2 numbers follow the same pattern.

    Don't worry. We'll find all of them.

    0511

  • Qs

    log 2000 = 3.30

    Name 2 parts to a log exponent.

    0512

  • log 2000 = 3.30

    1. Place Value Part2. Decimal for 1st digit .

    2 parts to a log exponent

    0513

  • log 2 = 0.30

    How can you remember log of 2?

    0514

  • log 2 = 0.30

    See 2, think 3.

    0515

  • log 4 = ?

    What's the log exponent for 4?

    0516

  • log 4 = 0.60

    Log of 4, base 10, is 0.60

    0517

  • log 4 = 0.60

    How can you remember log of 4?

    0518

  • 2 + 20.30 + 0.30

    Double 2 to find 4.

    log 4 = 0.60

    0519

  • 0520

  • Chapter 1 Lesson 4

    Basic Logarithms

    What are the log exponents of 3 and 6?

    0521

  • Okay, dokey. I've got logs of 2 and 4 down. What's the next log?

    0522

  • We'll find the log of 3.You have to remember it.

    0523

  • realnumber

    log exponent

    Log of 3 is 0 .48Remember this exponent.

    log 3 = 0.48≅

    0524

  • realnumber

    log exponent

    Got a memory trick for it?

    log 3 = 0.48≅

    0525

  • log 3 = 0.48 realnumber

    log exponent

    See 3, then think 4 and double 4 is 8.

    Sure, think about this.

    Time for a problem.

    0526

  • log 300

    What's the log exponent for 300?

    0527

  • log 300

    I'm guessing it starts with the place part.

    0528

  • 2 . ?

    log 300

    2 Places

    It's the log of 100, 2. What's the exponent for 3?

    0529

  • 2 . 482 Places The first

    digit is 3

    See 3, think 48.Ok, I get it now.

    0530

  • 2 . 482 Places The first

    digit is 3

    Same deal as the other logs.

    0531

  • log 300 = 2.48

    2 places and log of 3 is 0.48.

    Log of 300 is 2.48.

    0532

  • This can be habit forming. I'll make a bigger one.

    0533

  • log 3,000,000

    Find the log exponent for 3,000,000.

    0534

  • log 3,000,000

    This is almost like too easy.

    0535

  • 6 . 48

    log 3,000,000 = 6.48

    6 Places The first digit is 3

    6 places and 0.48 for 3.

    0536

  • log 3 = 0.48

    Can you use log of 3 to find other logs like 2 did?

    0537

  • log 3 = 0.48

    Abracadabra, log of 6. I'll start off with a trick.

    0538

  • Add 0.30

    log 3 = 0.48+ 0.30

    Exactly the same as finding log 4. So, what's the log of 6?

    0539

  • log 6 = 0.78

    This one is easy to remember.

    Add 0.48 to 0.30. It's 0.78

    0540

  • log 6 = 0.78

    How do you remember it?

    0541

  • log 6 = 0.78

    See log 6 and think 78 are next.

    0542

  • log 6 = 0.78

    Sure. Or you can add 0.30. I'll get another problem.

    0543

  • log 6000

    What's the log exponent?

    0544

  • log 6000

    Start with the place value part.

    That's a 3 for 1000.

    0545

  • 3 . ?3 Places The first

    digit is 6

    log 6000

    What's the decimal part?

    0546

  • log 6 = 0.78

    See the log of 6,then 78 are the decimals.

    It's so abc 's. I like that.Like 1,2,3 a,b,c.

    0547

  • log 6000 = 3.78

    ABC, 123. Michael Jackson would've liked that.

    0548

  • log 6000 = 3.78

    I'm so into the basics.Are we almost done?

    0549

  • log 600,000

    Find the log exponent for 600,000.

    All 1 step, do the answer.

    0550

  • Start w ith 0.48

    Add 0.30

    Here's the way you find it. Add 0.30, just like log 4.

    0551

  • Start w ith 0.48

    Add 0.30

    Finish this log equation off.

    0552

  • log 600,000 = 5.78

    I think 2 is my favorite one.

    0553

  • You can count your toes if that works.

    0554

  • 5 7 8 9

    So, where's 5, 7, 8, and 9?

    0555

  • Practice 2, 3, 4, and 6.We'll do those tomorrow.

    0556

  • Qs

    log 3 = 0.48

    What's the log exponent for 3?

    0557

  • log 3 = 0.48≅

    log of 3 is 48 100ths.

    0558

  • log 3 = 0.48≅

    How can you remember log 3?

    0559

  • log 3 = 0.48

    3 4 8Remember log 3, think...

    then and

    0560

  • log 6 = ?≅

    What's the log exponent for 6?

    0561

  • log 6 = 0.78≅

    log of 6 is 78 100ths.

    0562

  • log 6 = 0.78≅

    How can you remember it?

    0563

  • log 6 = 0.78

    6 78

    0.48 + 0.30

    You can count 6, 7, 8.

    then

    Or Add log of 2, 0.30.

    0564

  • 0565

  • Practice #1

    Chapter 1 Lesson 4

    Basic Logarithms

    Find the log exponent for numbers with 2, 4, 3 and 6.

    0566

  • log 2000 = 3.30

    Name 2 parts to a log exponent.

    0567

  • log 2000 = 3.30

    1. Place Value Part2. Decimal for 1st digit .

    2 parts to a log exponent

    0568

  • log 2 = 0.30

    How can you remember log of 2?

    0569

  • log 2 = 0.30

    See 2, think 3.

    0570

  • log 4 = ?

    What's the log exponent for 4?

    0571

  • log 4 = 0.60

    Log of 4, base 10, is 0.60

    0572

  • log 4 = 0.60

    How can you remember log of 4?

    0573

  • 2 + 20.30 + 0.30

    Double 2 to find 4.

    log 4 = 0.60

    0574

  • Problems

    log 2,000,000

    What's the 1st step to find a log exponent?

    0575

  • Log 2,000,000

    Find the place value part . What's the 2nd step?

    6.

    0576

  • Log 2,000,000

    6.30

    Log of 2,000,000, base 10, is 6.30.

    Decimal exponent for 2 .

    0577

  • What's the 1st step for log of 40,000?

    log 40,000

    0578

  • Log 40,000

    Find the place value part . What's the 2nd part?

    4.

    0579

  • Log 40,000

    Log of 40,000, base 10, is 4.60.

    4.60

    0580

  • log 2,000

    All in 1 step.What's the log exponent?

    0581

  • Log 2,000

    Log of 2,000, base 10, is 3.30.

    3.30

    0582

  • log 40,000

    All in 1 step.What's the log exponent?

    0583

  • Log of 40,000, base 10, is 4.60.

    4.60

    log 40,000

    0584

  • 0585

  • Practice #2

    Chapter 1 Lesson 4

    Basic Logarithms

    Find the log exponent for numbers with 2, 4, 3 and 6.

    0586

  • log 3 = 0.48

    What's the log exponent for 3?

    0587

  • log 3 = 0.48≅

    log of 3 is 48 100ths.

    0588

  • log 3 = 0.48≅

    How can you remember log 3?

    0589

  • log 3 = 0.48

    3 4 8Remember log 3, think...

    then and

    0590

  • log 6 = ?≅

    What's the log exponent for 6?

    0591

  • log 6 = 0.78≅

    log of 6 is 78 100ths.

    0592

  • log 6 = 0.78≅

    How can you remember it?

    0593

  • log 6 = 0.78

    6 78

    0.48 + 0.30

    You can count 6, 7, 8.

    then

    Or Add log of 2, 0.30.

    0594

  • Problems

    log 300,000

    Find the log exponent.

    5.30 5.48 5.60 5.78

    0595

  • Log 300,000, base 10, is 5.48.

    Log 300,000

    5.48

    0596

  • Find the log exponent.

    3.30 3.48 3.60 3.78

    log 6000

    0597

  • Log 6,000, base 10, is 3.78.

    Log 6000

    3.78

    0598

  • Find the log exponent.

    7.30 7.48 7.60 7.78

    log 30,000,000

    0599

  • Log 30,000,000, base 10, is 7.48.

    Log 30,000,000

    7.48

    0600

  • log 600

    Find the log exponent.How do you remember 6?

    0601

  • See 6, remember 78.Log 600, base 10, is 2.78.

    Log 600

    2.78

    0602

  • log 3,000

    Find the log exponent.

    0603

  • Log 3000, base 10, is 3.48.

    Log 3,000

    3.48

    0604

  • 0605

  • Performance #1

    Chapter 1 Lesson 4

    Basic Logarithms

    Find the log exponent for numbers with 2, 4, 3 and 6.

    0606

  • log 200 = x

    log 400 = x

    Find the log exponents.

    0607

  • log 200 = 2 .30

    log 400 = 2 .60

    0608

  • log 3000 = x

    log 60,000 = xFind the log exponents.

    0609

  • log 3000 = 3 .48

    log 60,000 = 4 .78

    0610

  • log 20 = x

    log 30 = x

    Find the log exponents.

    0611

  • log 20 = 1 .30

    log 30 = 1 .48

    0612

  • x10 = 40,000

    10 = 20,000Find the exponents.

    x

    0613

  • 10 = 40,000

    10 = 20,000

    4.60

    4.30

    0614

  • Find the exponents.

    x10 = 300

    10 = 600x

    0615

  • 10 = 300

    10 = 600

    2.48

    2.78

    0616

  • 10 = x

    10 = x

    2.30

    2.60

    0617

  • 10 = 2000

    10 = 4000

    2.48

    2.78

    0618

  • 0619

  • Performance #2

    Chapter 1 Lesson 4

    Basic Logarithms

    Find the log exponent for numbers with 2, 4, 3 and 6.

    0620

  • log 20 = x

    log 4,000 = x

    Find the log exponents.

    0621

  • log 20 = 1 .30

    log 4000 = 3 .60

    0622

  • log 30 = x

    log 6,000 = xFind the log exponents.

    0623

  • log 30 = 1 .48

    log 6000 = 3 .78

    0624

  • log 200 = x

    log 300 = x

    Find the log exponents.

    0625

  • log 200 = 2 .30

    log 300 = 2 .48

    0626

  • x10 = 4000

    10 = 2000Find the exponents.

    x

    0627

  • 10 = 4000

    10 = 2000

    3.60

    3.30

    0628

  • Find the exponents.

    x10 = 3000

    10 = 6000x

    0629

  • 10 = 3000

    10 = 6000

    3.48

    3.78

    0630

  • 10 = x

    10 = x

    3.48

    3.78

    0631

  • 10 = 3000

    10 = 6000

    3.48

    3.78

    0632

  • 0633

  • 1. The log for 7, 8, and 9?......6342. The log exponent of 5.........6853. Questions 1........................7104. Questions 2........................7335. Performance 1....................7506. Performance 2....................764

    Chapter 1 Lesson 5Basic Logarithms

    0634

  • Chapter 1 Lesson 5

    Basic Logarithms

    What are the log exponents for 7, 8, and 9?

    0635

  • I never thought it wouldtake so long to count to 9.

    0636

  • Well, 3 and 6 went together just like 2 and 4 did.

    But, the rest are different.

    0637

  • So, do you add 0.30 or what?

    0638

  • You add, but 7, 8, and 9 add a different number.

    I'll start off with log exponent for 8.

    0639

  • I know how to remember this.

    log 8 = 0.90≅

    0640

  • log 8 = 0.90

    With your brain.How about that 8 with a 9?

    0641

  • See 8, think 9.

    log 8 = 0.90≅

    That totally works.

    0642

  • log 8 = 0.90

    We'll do the log of 7 next.Another ABC, 1, 2, 3.

    0643

  • Ok, this is going to surprise you.

    log 7 = log 8 = 0.90 ≅

    0644

  • 7 takes 5 100ths away.

    log 7 = 0.85log 8 = 0.90

    How are you going to remember it?

    0645

  • log 7 = 0.85≅

    Kind of like 3 had 48.

    7, remember 8 and 5.

    0646

  • log 7 = 0.85≅

    Log of 9 does the same thing.

    What is that?

    0647

  • 9 adds 5 100ths.

    log 8 = 0.90log 9 = 0.95

    This one is easy to remember.

    0648

  • 9 is the only one that has the same digit next.

    log 9 = 0.95≅

    0649

  • log 7 = 0.85log 8 = 0.90log 9 = 0.95

    Add 0.05.

    Add 0.05.

    I told you it was different.

    0650

  • log 7 = 0.85log 8 = 0.90log 9 = 0.95

    Add 0.05.

    Add 0.05.

    Yeah, go over them again.

    0651

  • log 8 = 0.90

    Think about it my way.

    How do you find the log of 7?

    0652

  • log 7 = 0.85log 8 = 0.90≅

    Take 5 100ths away. That's 0.05.

    0653

  • log 7 = 0.85log 8 = 0.90≅

    Okay, Log of 9 is the easy one.

    0654

  • log 8 = 0.90log 9 = 0.95

    Add 5 100ths to log of 8.

    0655

  • log 8 = 0.90log 9 = 0.95

    How can you remember it?

    0656

  • log 9 = 0.95≅

    Only 9 has the same number as it's exponent.

    0657

  • log 9 = 0.95≅

    Now I'll do a few logs with it.

    0658

  • log 7,000

    Find the log exponent for 7,000.

    0659

  • log 7,000

    I've got to remember this.

    0660

  • 3 . 853 Places The first

    digit is 7and

    log 7,000 = 3.85≅

    85 takes 5 100ths away from 0.90.

    0661

  • Nice, now one with an 8.

    0662

  • log 800

    Find the log exponent for 800.

    0663

  • log 800

    Puts the easy in the cheezy.

    0664

  • 2 . 90

    log 800 = 2.90

    2 Places The first digit is 8

    and

    8, then 9. 8's my favorite.

    0665

  • Last one with you know what.

    0666

  • log 90,000,000

    Oooh, big number.

    0667

  • log 90,000,000

    Find the log exponent for 90,000,000.

    0668

  • 7 . 95

    log 90,000,000 = 7.95

    7 Places The first digit is 9

    and

    That went faster than 2s and 4s

    0669

  • I kind of like the 5 100ths part.

    0670

  • Log exponents is one of the most unusual things we've done in math.

    You have to admit.

    0671

  • I used to think subtraction was tough.

    0672

  • Qs

    What's the log exponent for 7?

    log 7 = ?≅

    0673

  • log 7 = 0.85≅

    Log of 7 is 85 100ths.How can you remember it?

    0674

  • log 7 = 0.85≅

    Remember...7 think 85

    0675

  • What's the log exponent for 8?

    log 8 = ?≅

    0676

  • log 8 = 0.90≅

    Log of 8 is 9 10ths.How do you remember it?

    0677

  • 8 90thenSee 8, remember 9.

    log 8 = 0.90≅

    0678

  • What's the log exponent for 9?

    log 9 = ?≅

    0679

  • log 9 = 0.95≅

    Log of 9 is 95 100ths.Why is it different?

    0680

  • log 9 = 0.95

    It's the only one with double digits. 9 follows 9.

    0681

  • log 7 = 0.85log 8 = 0.90log 9 = 0.95

    Start at log 7. How do you get 8 and 9?

    0682

  • log 7 = 0.85log 8 = 0.90log 9 = 0.95

    Add 0.05 to each

    Add 0.05

    Add 0.05

    0683

  • 0684

  • Chapter 1 Lesson 5a

    Basic Logarithms

    What is the log exponent of 5?

    0685

  • I think we've got all of the log exponents.

    0686

  • Who taught you to count?

    0687

  • Actually, that was you.

    0688

  • Well, I did a terrible job.Log of 5 is one you remember.

    Here it is....

    0689

  • log 5 = 0.70

    They're both odd numbers.

    It equals 70 100ths.

    0690

  • log 5 = 0.70

    Actually, there is a way to use log of 4 to remember it.

    0691

  • log 4 = 0.60

    Remember 4, 5makes exponent 6, 7.

    log 5 = 0.70≅

    0692

  • log 4 = ?

    It also works if you can't remember log of 4.

    log 5 = 0.70≅≅

    0693

  • log 4 = ?log 5 = 0.70≅

    It's alittle late for that.

    0694

  • log 4 = 0.60log 5 = ?

    Okay, what's the log of 5?

    0695

  • log 5 = 0.70≅

    Duh, we just did this. Log of 5 is 0.70.

    0696

  • log 5 = 0.70≅

    Just checking. I'll make a problem.

    0697

  • What is the log exponent?

    log 50,000

    0698

  • Log 50,000 = 4.70

    Logarithm of 50,000, base 10, is 4 .70.

    I thought Log of 5 would be 0.5.

    0699

  • log 5 = 0.70

    All logs are alittle higher.

    Think of it's exponent form.

    0700

  • 10 = 50.7log 5 = 0.70

    Like all the others, the logarithm shows the exponent.

    0701

  • Decimal Log Exponents

    Finally, all the log exponents done. It took like a year.

    0702

  • You'll like the next part.We get to go backwards.

    0703

  • Qs

    log 5 = ?What's the log exponent of 5?

    0704

  • How can you remember log 5?

    log 5 = 0.70

    The log of 5 is 0 .7 10ths.

    0705

  • log 5 = 0.70≅

    They're both odd numbers.

    0706

  • log 4 = ?log 5 = ?

    How can you use log 4 to remember 5?

    0707

  • log 4 = 0.60log 5 = 0.70

    It goes 4, 5, then 6, 7.

    0708

  • 0709

  • Practice #1

    Chapter 1 Lesson 5

    Basic Logarithms

    What are the log exponents for 5, 7, 8, and 9?

    0710

  • What's the log exponent for 7?

    log 7 = ?≅

    0711

  • log 7 = 0.85≅

    Log of 7 is 85 100ths.How can you remember it?

    0712

  • log 7 = 0.85≅

    Remember...7 think 85

    0713

  • What's the log exponent for 8?

    log 8 = ?≅

    0714

  • log 8 = 0.90≅

    Log of 8 is 9 10ths.How do you remember it?

    0715

  • 8 90thenSee 8, remember 9.

    log 8 = 0.90≅

    0716

  • What's the log exponent for 9?

    log 9 = ?≅

    0717

  • log 9 = 0.95≅

    Log of 9 is 95 100ths.Why is it different?

    0718

  • log 9 = 0.95

    It's the only one with double digits. 9 follows 9.

    0719

  • log 7 = 0.85log 8 = 0.90log 9 = 0.95

    Start at log 7. How do you get 8 and 9?

    0720

  • log 7 = 0.85log 8 = 0.90log 9 = 0.95

    Add 0.05 to each

    Add 0.05

    Add 0.05

    0721

  • Find the log exponent.

    6.70 6.85 6.90 6.95

    Problems

    log 7,000,000

    0722

  • Log of 7,000,000, base 10, is 6.85.

    Log 7,000,000

    See 7, think 85.

    6.85

    0723

  • Find the log exponent.

    4.70 4.85 4.90 4.95

    log 50,000

    0724

  • Log 50,000

    Both 5 and 7 are odd.

    4.70

    Log of 50,000, base 10, is 4.70.

    0725

  • log 800

    Find the log exponent.How do you remember 8?

    0726

  • 2.90

    Log 800

    Log of 800, base 10, is 2.90.

    See 8, 9 is after it .

    0727

  • Find the log exponent. Why is 9 different?

    log 90,000

    0728

  • 4.95

    Log 90,000

    Log of 90,000, base 10, is 4.95.

    Only 9 starts the same, 95.

    0729

  • log 500,000

    Find the log exponent.How can you remember 5?

    0730

  • 5.70

    Log 500,000

    Log of 500,000, base 10, is 5.70.

    5 and 7, they're both odd.

    0731

  • 0732

  • Practice #2

    Chapter 1 Lesson 5

    Basic Logarithms

    What are the log exponents for 5, 7, 8, and 9?

    This lesson is different from the first.

    0733

  • log 5 = ?What's the log exponent of 5?

    0734

  • How can you remember log 5?

    log 5 = 0.70

    The log of 5 is 0 .7 10ths.

    0735

  • log 5 = 0.70≅

    They're both odd numbers.

    0736

  • log 4 = ?log 5 = ?

    How can you use log 4 to remember 5?

    0737

  • log 4 = 0.60log 5 = 0.70

    It goes 4, 5, then 6, 7.

    0738

  • Find the log exponent.

    5.70 5.85 5.90 5.95

    Problems

    log 500,000

    0739

  • Log of 500,000, base 10, is 5.70.

    Log 500,000

    5.70

    0740

  • Find the log exponent.

    3.30 3.48 3.60 3.78

    log 4,000

    0741

  • Log 4,000

    3.60

    Log of 4,000, base 10, is 3.60.

    0742

  • log 9000

    Find the log exponent.

    0743

  • 3.95

    Log 9000

    Log of 9000, base 10, is 3.95.

    0744

  • Find the log exponent.

    log 200,000

    0745

  • 5.30

    Log 200,000

    Log of 200,000, base 10, is 5.30.

    0746

  • log 3,000,000

    Find the log exponent.

    0747

  • 6.48

    Log 3,000,000

    Log of 3,000,000, base 10, is 6.48.

    0748

  • 0749

  • Performance #1

    Chapter 1 Lesson 5

    Basic Logarithms

    What are the log exponents for 5, 7, 8, and 9?

    0750

  • log 8000 = x

    log 7000 = x

    Find the log exponents.

    0751

  • log 8000 = 3 .90

    log 7000 = 3 .85

    0752

  • log 50 = x

    log 9,000 = x

    Find the log exponents.

    0753

  • log 50 = 1 .70

    log 9000 = 3 .95

    0754

  • log 80,000 = x

    log 90,000 = xFind the log exponents.

    0755

  • log 80,000 = 4 .90

    log 90,000 = 4 .95

    0756

  • x10 = 70

    10 = 80x

    Find the real numbers.

    0757

  • 1.85

    1.90

    10 = 70

    10 = 80

    0758

  • x10 = 500

    10 = 900x

    Find the real numbers.

    0759

  • 2.70

    2.95

    10 = 500

    10 = 900

    0760

  • x10 = 700

    10 = 800x

    Find the real numbers.

    0761

  • 2.8510 = 700

    10 = 8002.90

    0762

  • 0763

  • Performance #2

    Chapter 1 Lesson 5

    Basic Logarithms

    What are the log exponents for 5, 7, 8, and 9?

    0764

  • log 80 = x

    log 90 = x

    Find the log exponents.

    0765

  • log 80 = 1 .90

    log 90 = 1 .95

    0766

  • log 700 = x

    log 90,000 = x

    Find the log exponents.

    0767

  • log 700 = 2 .85

    log 90,000 = 4 .95

    0768

  • log 50,000 = x

    log 70,000 = xFind the log exponents.

    0769

  • log 50,000 = 4 .70

    log 70,000 = 4 .85

    0770

  • x10 = 700

    10 = 800x

    Find the real numbers.

    0771

  • 2.8510 = 700

    10 = 8002.90

    0772

  • x10 = 8000

    10 = 9000x

    Find the real numbers.

    0773

  • 3.9010 = 8000

    10 = 90003.95

    0774

  • x10 = 50,000

    10 = 70,000x

    Find the real numbers.

    0775

  • 4.7010 = 50,000

    10 = 70,0004.85

    0776

  • 0777

  • 1. Name 2 steps to find a real number..7782.3. Questions 1......................................8184. Questions 2......................................8375. Performance 1.................................8566. Performance 2.................................870

    Chapter 1 Lesson 6Basic Logarithms

    0778

  • Chapter 1 Lesson 6

    Basic Logarithms

    Name 2 steps to find the real number for a log exponent.

    0779

  • Going Backw ards

    How does a log go backwards?

    0780

  • You know the log exponent. Find it's real number.

    Sounds like a joke.

    Here's a problem.

    0781

  • log x = 1.60

    See, something like this. It finds the real number.

    0782

  • log x = 1.60

    Do I find the place value or the decimal part first?

    0783

  • log x = 1.60

    Either is fine, but, since we read numbers left to right, we'll start with the decimal part first.

    What does the decimal 0.60 find?

    0784

  • log x = 1.60

    Easy sneezy. 0.60 is log 4.

    4____

    0785

  • log x = 1.60

    4____So, what does the 1 show you?

    0786

  • log 40 = 1.60

    1 means there's 1 place, so the real number is 40.

    40I t counts place value.

    0787

  • log 40 = 1.60

    That's how you find thereal number from an exponent.

    40

    Here's another one...

    0788

  • log x = 2.30

    Find the real number thatmakes this logarithm (base 10).

    What's the first digit?

    0789

  • log x = 2.30

    2___

    The number for 0.30 is 2.

    0790

  • log x = 2.30

    What's the place value part?

    2___

    0791

  • log 200 = 2.30

    2 places is hundreds.

    0792

  • This one was easybecause you learned 2 first.

    log 200 = 2.30

    0793

  • Another real number, (base 10).

    What's the 1st digit?

    log x = 3.60

    0794

  • The number for 0.60 is 4.

    log x = 3.60

    4___

    0795

  • log x = 3.60

    What's the place value part?

    4___

    0796

  • log 4000 = 3.60

    3 places makes thousands.

    0797

  • log 4000 = 3.60

    log of 4000, base 10, is 3.60

    0798

  • Find the real number, all 1 step.

    log x = 4.90

    0799

  • log 80,000 = 4.90

    It's 8 and 4 places is 10,000.

    0800

  • log 80,000 = 4.90

    Log of 80,000, base 10, is 4.90.

    0801

  • Find the real number, all 1 step.

    log x = 6.85

    That's why I call it going backwards.

    0802

  • log 7,000,000 = 6.85

    It's 7 and 6 places is millions.

    0803

  • log 7,000,000 = 6.85

    log of 7 million, base 10, is 6.85.

    0804

  • 1. Decimal is 1st digit .2 . Place Value

    Why do you find the 1st digit first?

    0805

  • It's just how we say numbers.The 1st digit always goes first.

    0806

  • 1. Decimal is 1st digit .2 . Place Value

    Oh, that makes sense.

    0807

  • Wow. That's the 1st time you said something makes sense in logs.

    0808

  • I didn't say that logs make sense. Just how you say a number.

    0809

  • Well, at least something makes sense.

    0810

  • Qs

    log x = 1.60

    What's the 1st step to find a real number from an exponent?

    0811

  • log x = 1.60

    0.60 is log 4.

    4____Start w ith the 1st digit .

    0812

  • log x = 1.60

    What happens after the 1st digit?

    4____

    0813

  • log 40 = 1.60

    Count the place value.

    40

    1 means it's 40.

    0814

  • Name 2 steps to find a real number from a log exponent.

    log ? = 1.48

    0815

  • 1. Find the 1st digit.2. Find the places after it.

    log 30 = 1.48Start here.

    0816

  • 0817

  • Chapter 1 Lesson 6

    Basic Logarithms

    Practice #1 Name 2 steps to find the real number for a log exponent.

    0818

  • log x = 1.60

    What's the 1st step to find a real number from an exponent?

    0819

  • log x = 1.60

    0.60 is log 4.

    4____Start w ith the 1st digit .

    0820

  • log x = 1.60

    What happens after the 1st digit?

    4____

    0821

  • log 40 = 1.60

    Count the place value.

    40

    1 means it's 40.

    0822

  • Name 2 steps to find a real number from a log exponent.

    log ? = 1.48

    0823

  • 1. Find the 1st digit.2. Find the places after it.

    log 30 = 1.48Start here.

    0824

  • Problems

    What's the 1st step to find the real number?

    log x = 3.30

    0825

  • Log 2____ = 3.30

    What's the rest of the number?

    The decimal show s 2.

    0826

  • Log 2,000 = 3.30

    Logarithm of 2,000, base 10, is 3.30.

    Find the place value.

    0827

  • log x = 1.48

    All in 1 step, find the real number.

    0828

  • Log 30 = 1.48

    Logarithm of 30, base 10, is 1.48.

    0829

  • log x = 3.78

    Find the real number.

    0830

  • Log 6,000 = 3.78

    Logarithm of 6,000, base 10, is 3.78.

    0831

  • log x = 7.60

    Find the real number.

    0832

  • Log 40,000,000 = 7.60

    Logarithm of 40,000,000 base 10, is 7.60.

    0833

  • log x = 2.48

    Find the real number.

    0834

  • Log 300 = 2.48

    Logarithm of 300, base 10, is 2.48.

    0835

  • 0836

  • Chapter 1 Lesson 6

    Basic Logarithms

    Practice #2 Name 2 steps to find the real number for a log exponent.

    0837

  • Qs

    log x = 1.60

    What's the 1st step to find a real number from an exponent?

    0838

  • log x = 1.60

    0.60 is log 4.

    4____Start w ith the 1st digit .

    0839

  • log x = 1.60

    What happens after the 1st digit?

    4____

    0840

  • log 40 = 1.60

    Count the place value.

    40

    1 means it's 40.

    0841

  • Name 2 steps to find a real number from a log exponent.

    log ? = 1.48

    0842

  • 1. Find the 1st digit.2. Find the places after it.

    log 30 = 1.48Start here.

    0843

  • Problems

    What's the 1st step to find the real number?

    log x = 4.85

    0844

  • Log 7____ = 4.85

    What's the rest of the number?

    The decimal show s 7.

    0845

  • Log 70,000 = 4.85

    Logarithm of 70,000, base 10, is 4.85.

    Find the place value.

    0846

  • log x = 2.85

    All in 1 step, find the real number.

    0847

  • Log 700 = 2.85

    Logarithm of 700, base 10, is 2.85.

    0848

  • log x = 5.95

    Find the real number.

    0849

  • Log 900,000 = 5.95

    Logarithm of 900,000, base 10, is 5.95.

    0850

  • log x = 4.70

    Find the real number.

    0851

  • Log 50,000 = 4.70

    Logarithm of 50,000 base 10, is 4.70.

    0852

  • log x = 3.60

    Find the real number.

    0853

  • Log 4,000 =


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