Objectives:1. Be able to convert a logarithmic function into an

exponential function. 2. Be able to convert an exponential function into a

logarithmic function. 3. Be able to convert a natural log (ln) into an exponential

function. 4. Be able to evaluate log functions using the same base

formula. Critical Vocabulary:

Logarithmic Function, Natural Log, Exponential Function

I. Convert from a log into exponential a. Formula: y = loga x x

= ay b. Examples 1. loga 7 =

12 Solution: 7 = a12 2. log4 x =

8 Solution: x = 48 II. Convert from an exponential into a

log a. Formula: x = ay loga x = yb. Examples 1. a4 =

9 Solution: loga 9 = 4 2. 5x =

12 Solution: log5 12 = x

III. Natural Log into an exponential function a. Formula: y = ln x x

= ey b. Examples

1. ln 5 = x Solution: 5 =

ex 2. ln x = 7 Solution: x = e7

3. ex = 21 Solution: ln 21 =

x

IV. Evaluating Logs a. Same base

formula 1. Formula: If au = av, Then u = v

1. 3x = 9 Solution: x =

2 2. log2 4 = x

Solution: x = 2

b. Examples

Solution: x = -1

3x = 32

2x = 4 2x = 22

3x = 1/3

3. log3 (1/3) = x

3x = 3-

1

4. log8 16

Solution: x = 4/3

5. log4 2

6. log9 (1/3)

Solution: x = -1/2

8x = 16 23x = 24 3x = 4

4x = 2 22x = 2 2x = 1

Solution: x = 1/2

9x = 1/3 32x = 3-

1 2x = -1

IV. Evaluating Logs

7. log1/27 9

8. 81log3

Solution: x = 8

(1/27)x = 9 27-1x = 9 3-3x = 32 -3x = 2 Solution: x = -

2/3

813 x

42 33 x

42

x

IV. Evaluating Logs

8.

Homework:Page 503-504 #3 – 27 odds, 37-43 odds, 55,

57