1. Example 1 LOGARITHMIC FORM EXPONENTIAL FORM a. log2 16 = 4 24 = 16 b.
Rewrite Logarithmic Equations
LOGARITHMIC FORM
EXPONENTIAL FORM a.
log2 16 = 4 24 = 16 b.
log7 1 = 70 = 1 c.
log5 5 = 1 51 = 5 d.
log 0.01 = 2 – =
0.01
10 2 – = 4 1 – e.
log1/4 4 = 1 –

2. Rewrite the equation in exponential form.
Checkpoint
Rewrite Logarithmic Equations
Rewrite the equation in exponential form. 1.
log3 81 = 4
ANSWER 34 = 81 2.
log4 4 = 1 41 = 4
ANSWER 3.
log6 1 = 60 = 1
ANSWER = 4 2 1 –
ANSWER
log1/2 4 4. = 2 –

3. Evaluate the expression.
Example 2
Evaluate Logarithmic Expressions
Evaluate the expression. a.
log4 64 b.
log4 2 c.
log1/3 9
SOLUTION
To help you find the value of logb y, ask yourself what power of b gives you y. a. 4? = 64
What power of 4 gives 64? 43 = 64
Guess, check, and revise.
Definition of logb y
log4 64 = 3 3

4. Example 2
Evaluate Logarithmic Expressions b. 4? = 2
What power of 4 gives 2?
41/2 = 2
Guess, check, and revise.
Definition of logb y
log4 2 = 2 1 c. = 9 3 1
What power of gives 9? ? = 9 3 1 – 2
Guess, check, and revise.
log1/3 9 = 2 –
Definition of logb y 4

5. Example 3 a. Evaluate 10log 6. b. Simplify log2 8x. SOLUTION
Use Inverse Properties
a. Evaluate 10log 6.
b. Simplify log2 8x.
SOLUTION
a. 10log 6 = 10
log10 6 6 =
b. log2 8x =
log x ( ) 23 =
log2
23x = 3x 5

6. Checkpoint 5. Evaluate log2 64. 6 ANSWER 6. Evaluate log4 16 1 .
Evaluate and Simplify Logarithmic Expressions
5. Evaluate log2 64. 6
ANSWER
6. Evaluate log4 16 1 .
ANSWER 2 –
ANSWER 2 1
7. Evaluate log16 4.
8. Simplify
log7 x x
ANSWER
9. Simplify log5 25x. 2x
ANSWER

7. Checkpoint 6x 10. Simplify log2 64x. ANSWER
Evaluate and Simplify Logarithmic Expressions
10. Simplify log2 64x. 6x
ANSWER

8. For both graphs, find the two key points where and where = y 1.
Example 4
Graph Logarithmic Functions
Graph the function. Describe the vertical asymptote. State the domain and range. a. y =
log3 x b. y =
log3 ( x – 2 )
SOLUTION
For both graphs, find the two key points where and where = y 1.
Let Then ,
so is on the graph. = x 1. y
log3 1 ( )
1, 0
Let Then ,
so is on the graph. = x 3. y
log3 3 1 ( )
3, 1 8

9. Example 4
Graph Logarithmic Functions
The vertical asymptote is the y-axis. The domain is , and the range is all real numbers. x
>
b. Let Then ,
so is on the graph. = x 3. ( )
3, 0 3 – y
log3 2
Let Then
so is on the graph. = x 5. ( )
5, 1 1, 5 – y
log3 2
The vertical asymptote is The domain is , and the range is all real numbers. 2
> x = 2. 9

10. ; domain: , range: all real numbers = x >
Checkpoint
Graph Logarithmic Functions
Graph the function. Describe the vertical asymptote. State the domain and range.
11. y =
log10 x
ANSWER
; domain: , range: all real numbers = x
>

11. ; domain: , range: all real numbers = x 3 >
Checkpoint
Graph Logarithmic Functions
Graph the function. Describe the vertical asymptote. State the domain and range.
12. x – = y
log2 ( ) 3
ANSWER
; domain: , range: all real numbers = x 3
>

12. ; domain: , range: all real numbers = x >
Checkpoint
Graph Logarithmic Functions
Graph the function. Describe the vertical asymptote. State the domain and range.
13. y =
log5 x + 3
ANSWER
; domain: , range: all real numbers = x
>