9.3 1

Section 9.3 Logarithmic Functions Graphs of Logarithmic Functions Log2x Equivalent Equations Solving Certain Logarithmic Equations

9.3 2

Inverses of Exponential Functionsf(x) = 2 x f -1(x) = ? x = 2 y

Logarithmic Functions:

Ranges are Exponents

Notation:

f -1(x) = log2x

“the log, base 2, of x …”

means: the exponent of 2 needed to get x”

9.3 3

Evaluating Log Expressions

7.3)162,82(13213log

3222log

022121log

52232232log

43

2

381

81

2

0

2

5

2

y

y

y

y

y

yy

yy

yy

9.3 4

General Definition of Logarithms

3125log2100log

32log

02:0log

510

2

2

impossiblealso

solutionnoimpossible y

9.3 5

“A Logarithm is an Exponent” Simplify:

xxfxffandxfthenxxfif

x

x

7

2

7

log

7

11

1

7

13log

85log

7)(log))((7)(log)(

132

857

9.3 6

Graphing – Make Table of Many Points

9.3 7

Equivalent Equations (MEMORIZE)

dbda

a

y

ab

a

y

log

77log2

535log

2

3

bcca

y

x

ab

y

x

log

14log4

8log28

1

2

9.3 8

Solving Certain Log Equations Rewrite them as equivalent exponential equations:

x

x

x

x

81

3

3

2

2

1

2

3log

?4

4

4

16

216log

22

2

tooxnotwhy

x

x

x

x

9.3 9

Principle of Exponential Equality

}110|{1log

}110|{101log

044141log

310101000101000log

1

0

04

310

aandaaaaa

aandaaa

tt

xx

a

a

tt

xx

9.3 10

What Next? Parabolas, Circles, Ellipses Chapter 10