AGENDA · *Ifyou3finishearly,trythisone!. log 2 (7x) ≠ log 2 7 - log 2 x like the student said....

Logarithms Unit

1

Day 2

AGENDAObjective:SWBAT simplify and evaluate expressions involving logarithms and properties of logarithms

Language Objective: SWBAT identify the error in an a sample problem by writing an explanation of the error as well as the correct method for solving the problem in a Think...Write..Pair...Share activity with a partner

1) Take out HW to be checked 2) Do Now3) Discover: Properties of LogarithmsGroups: product & quotient propertiesClass: Power property

4)Try some! (practice)5) Think...Write...Pair...Share6) Practice7) Exit Ticket

HW: "Logs worksheet #2"

Logarithms Unit

2

Day 2

DO NOW!

1) Write in logarithmic form: 4² = 16 → _________________________

2) Write in exponential form: log₇(⅟₄₉) = -‐2 → ___________________

3) Solve for the variable: (Hint -‐ switch to exponential form.)

a) log₂16 = x b) log₉n = 2 c) logb1,000,000 = 6

d) log₄n = 0 e) log₇1 = x f) logb(⅛) = 3

• Write equivalent forms for exponential and logarithmic equations• Use the common log function to solve exponential and logarithmic equations• Simplify and evaluate expressions involving logarithms and the properties of logarithms• Use the definitions of exponential and logarithmic functions to solve equations• Graph exponential and logarithmic functions• Model and solve real-‐world problems involving exponential and logarithmic

relationships

.

Logarithms Unit

3

Day 2

DO NOW!

1) Write in logarithmic form: 4² = 16 → _________________________

2) Write in exponential form: log₇(⅟₄₉) = -‐2 → ___________________

3) Solve for the variable: (Hint -‐ switch to exponential form.)

a) log₂16 = x b) log₉n = 2 c) logb1,000,000 = 6

d) log₄n = 0 e) log₇1 = x f) logb(⅛) = 3

• Write equivalent forms for exponential and logarithmic equations• Use the common log function to solve exponential and logarithmic equations• Simplify and evaluate expressions involving logarithms and the properties of logarithms• Use the definitions of exponential and logarithmic functions to solve equations• Graph exponential and logarithmic functions• Model and solve real-‐world problems involving exponential and logarithmic

relationships

.

log416 =2

7-2= 1/49

2x= 16x = 4

92= nn = 18

b6= 1,000,000b = 10

40= nn = 1

7x= 1x = 0

b3= 1/8b = 2

Logarithms Unit

4

Day 2

.

Logarithms Unit

5

Day 2

.

Logarithms Unit

6

Day 2

.

Logarithms Unit

7

Day 2

.

log32 log49

log5162log55 = 1

logb(uv/uw)

= logb(v/w)

logb(4x∙y/3y)

logb(4x/3)

Logarithms Unit

8

Day 2

Properties of Logs Product Property logb(m ⋅ n) = logbm + logbn

Quotient Property .

Power Property logb(m p) = p·logbm

where m > 0, n > 0, b > 0 and b ≠1(all values are positive and b ≠1)

Why do you think this is?Lets prove the rule together!

bx = m

.

Logarithms Unit

9

Day 2

Why do you think this is?Lets prove the rule together!

bx = m

Properties of Logs Product Property logb(m ⋅ n) = logbm + logbn

Quotient Property .

Power Property logb(m p) = p·logbm

where m > 0, n > 0, b > 0 and b ≠1(all values are positive and b ≠1)

Logarithms Unit

10

Day 2

Try Some!

Logarithms Unit

11

Day 2

Try Some! (Answers)

Logarithms Unit

12

Day 2

Think...Write...Pair...Share

*If you finish early, try this one!

.

Logarithms Unit

13

Day 2

Think...Write...Pair...Share

*If you finish early, try this one!

.

log2(7x) ≠ log27 - log2x like the student said.

log2(7x) = log27 + log2x

We can factor x2 +2xy + y2 to get (x+y)2.

So log3(x2 +2xy + y2 ) = log3(x+y)

2.

The power property allows log3(x+y)2 = 2∙log3(x+y).

Therefore, log3(x2 +2xy + y2 ) =2∙log3(x+y).

Logarithms Unit

14

Day 2

Practice Problems

Logarithms Unit

15

Day 2

Practice Problems

log415

log914

log914

log1255

log314

log5198

log76

log563

log211-log22 = log211 - 1

log24-log27 = 2- log27

log216-log25 = 4 - log25

log29-log25

log218-log27

log225-log23

log3(2)

log5(6/11)

log3(3) = 1

log7(2)

log3(4)

log5(4)

Logarithms Unit

16

Day 2

Practice Problems continued....

Logarithms Unit

17

Day 2

Practice Problems continued....

3∙log25

12∙log264= 12∙6 = 72

4∙log39= 4∙2 = 8

10∙2= 20

7∙3 = 21

20∙log315

100∙logba

10∙logbx

x∙logby

9∙logbt

3∙logbx

5∙logbb =5∙1 = 5

Logarithms Unit

18

Day 2

Score: ________/ 6 Name __________________________

Exit Ticket

1) Simplify: log25 + log26

2) Simplify: log25 -‐ log26

3) Simplify: log2(56)

Score: ________/ 6 Name __________________________

Exit Ticket




Logarithms Unit

19

Day 2

Score: ________/ 6 Name __________________________

Exit Ticket




Score: ________/ 6 Name __________________________

Exit Ticket




log2(30)

log2(5/6)

6∙log2(5)

log3(63)

log3(9/7)

7∙log3(9)

Logarithms Unit

20

Day 2

HW: "Logs worksheet #2"1) Write the following in Logarithmic Form

25 = 32 _____________ (2 pt)

2) Write the following in Exponential Form log416 = 2 _____________ (2 pt)

3) Solve the following for x. (1 pt each)

a) 2x = ⅛ b) x3 = 27 c) 9½ = x

x = _______ x = ______ x = ______


a) 10x = 57 b) log₁₀(12,345) = x c) log(0.10) = x

x = _______ x = ______ x = ______


a) x = log₁₀(100) b) x = log₁₁(121) c) log₄(64) = x

x = _______ x = ______ x = ______

Logarithms Unit

21

Day 2

HW: "Logs worksheet #2"1) Write the following in Logarithmic Form

25 = 32 _____________ (2 pt)

2) Write the following in Exponential Form log416 = 2 _____________ (2 pt)


a) 2x = ⅛ b) x3 = 27 c) 9½ = x

x = _______ x = ______ x = ______


a) 10x = 57 b) log₁₀(12,345) = x c) log(0.10) = x

x = _______ x = ______ x = ______


a) x = log₁₀(100) b) x = log₁₁(121) c) log₄(64) = x

x = _______ x = ______ x = ______

log232=5

42 = 16

-3 3 3

2 2 3

-1

Logarithms Unit

22

Day 2

HW: "Logs worksheet #2" continued...

I. Simplify the following: (Product &Quotient properties)

1) log2(5) + log2(7) = _____________________________________

2) log3(45) -‐ log3(5) = ____________________________________

3) log7(3x) -‐ log7(9x) + log7(6y) = ______________________________

2) log2(5) + log3(45) = _____________________________________

II. Simplify the following: (Power property)

1) log5254 = _____________________________________

2) log327100 = ____________________________________

3) log445 = ______________________________

4) log10102 = ______________________________

III. Simplify the following: (*Challenge)

*5) Solve for x: 9log92 = x __________________________________

*6) Solve for x: 5log53 = x __________________________________

*7) Write as a single log: 5∙log2m + 2∙log2n =

________________________________

Logarithms Unit

23

Day 2

HW: "Logs worksheet #2" continued...

I. Simplify the following: (Product &Quotient properties)

1) log2(5) + log2(7) = _____________________________________

2) log3(45) -‐ log3(5) = ____________________________________

3) log7(3x) -‐ log7(9x) + log7(6y) = ______________________________

2) log2(5) + log3(45) = _____________________________________

II. Simplify the following: (Power property)

1) log5254 = _____________________________________

2) log327100 = ____________________________________

3) log445 = ______________________________

4) log10102 = ______________________________

III. Simplify the following: (*Challenge)

*5) Solve for x: 9log92 = x __________________________________

*6) Solve for x: 5log53 = x __________________________________

*7) Write as a single log: 5∙log2m + 2∙log2n =

________________________________

log235

log39 = 2

log72y

log25 +log345

4∙2= 8

100∙3 = 300

5∙1 = 5

2∙1 = 2

log9x = log92 → x=2

log5x = log53 →x=3

log2m5 + log2n

2 = log2(m5∙n2)

Date post:	14-Oct-2020
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AGENDA · *Ifyou3finishearly,trythisone!. log 2 (7x) ≠ log 2 7 - log 2 x like the student said....

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