Notes Over 5.2Rewriting Logarithmic Equations

364log .1 4 4

and

3 643125log .2 5

53 125

1log .3 7

7 0 1 8

1log .4 2

23

8

1

xy alog yax Rewrite the equation in exponential form.

are equivalent.

Evaluate each logarithm.

0 3

Notes Over 5.2Properties of Logarithms

.1 01log a 1 because 0 a

.2 1log aa aa 1 because

.3 xa xa log xa xa log because

.4 yx aa loglog If yx then

5loglog .5 77 xUse properties to solve.

5xx 5

33log .65x

Notes Over 5.2Graphing Logarithmic Functions

xxf 2 .7 Graph both functions on the same graph.

x y

2 4/11

012

2/1124

xxg 2logx y

4/1 22/1

124

1012

Notes Over 5.2Common and Natural Logarithms

25log .8 10

397.13.0ln .9

204.1

e

1ln .11

xy 10logUse a calculator to evaluate.

Use properties to simplify.

1ln e

xy elog xlnx log

21ln .10 881.0

13

1ln .12

3

0 0

Notes Over 5.2Graphing Logarithmic Functions

xxf ln .13 Graph the logarithmic function.

x y

2135.1

012

368.172.239.7

Inverse of xey

sticscharacteriDomain:

Range:x-int:

Inc/Dec:

asymp:

Contin:

,0 ,

1increasing

0xcontinuous

Notes Over 5.2Graphing Logarithmic Functions

2 log .14 4 xy

Graph the function.

x y

1 04 1

xy 4 of Inverse

Move curve 2 units to the left.

Asymptote: 2x

Notes Over 5.2