10.2 Logarithms and Logarithmic functions

Graphs of a Logarithmic function verse Exponential functions

In RED y = 10x

Graphs of a Logarithmic function verse Exponential functions

In RED y = 10x , In Blue y = Log x

The functions relate in which way?

The Main Concept of Logarithms

Remember the way an exponential function and a Logarithm function is related.

92931,0

32 Log

bbxLOGyxb b

y

The Main Concept

Remember

1,0

bbxLOGyxb b

y

Write in Exponential form

Log 4 16 = 2

21001

10 Log

Write in Exponential form

Log 4 16 = 2

21001

10 Log

1642

100110 2

Write in Logarithmic form

53 = 125

327 31

Write in Logarithmic form

53 = 125

327 31

3125log5

313log27

How to use the Concept to Solve problems

Evaluate

243log3


Evaluate

5

332433

243log

243log

5

3

3

x

x

x

x


Evaluate 99Log


Evaluate

1

99

9

9

1

9

9

x

xLog

Log

x


Evaluate kx 1log 277


Evaluate

1

1loglog

7

2

277

1log 27

xk

xk

kx

Use the concept

Solve 34log8 n

Use the concept

Solve

16

8

34log

34

8

n

n

n

Use the concept

Solve 3log6 x

Use the concept

Solve

02166

3log

3

6

xx

x

Why Greater then Zero?

Solve for x

Check your solutions

34loglog 42

4 xx

Solve for x


3,1

031034

34

34loglog

2

2

42

4

x

xxxx

xx

xx

Solve for x


3,1

031034

34

34loglog

2

2

42

4

x

xxxx

xx

xx

9log9log

334log3log

1log1log314log1log

44

42

4

44

42

4

They both work. What would make the answers not work?

This Logarithm is impossible

Why?

)27(3 Log

This Logarithm is impossible

Try to solve

,273

273

x

xLog

Is there any x that would make it equal -27?

How do you solve

Evaluate the expression

125log5

How do you solve

Evaluate the expression

351255

125log

125log

3

5

5

x

x

x

Homework

Page 536# 21 – 39 odd,

47 – 59 odd

Homework

Page 536# 22 – 40 odd,

48 – 58 odd

10.2 Logarithms and Logarithmic functions

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