Notes Over 5.2

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Notes Over 5.2 Rewriting Logarithmic Equations 3 64 log . 1 4 4 and 3 64 3 125 log . 2 5 5 3 125 1 log . 3 7 7 0 1 8 1 log . 4 2 2 3 8 1 x y a log y a x Rewrite the equation in exponential form. are equivalent . Evaluate each logarithm. 0 3

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Notes Over 5.2. Rewriting Logarithmic Equations. and. are equivalent. Rewrite the equation in exponential form. Evaluate each logarithm. Notes Over 5.2. Properties of Logarithms. Use properties to solve. Notes Over 5.2. Graphing Logarithmic Functions. - PowerPoint PPT Presentation

Transcript of Notes Over 5.2

Page 1: Notes Over 5.2

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

Page 2: Notes Over 5.2

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

Page 3: Notes Over 5.2

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

Page 4: Notes Over 5.2

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

Page 5: Notes Over 5.2

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

Page 6: Notes Over 5.2

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

Page 7: Notes Over 5.2

Notes Over 5.2