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 =