1. Logarithmic Functions
Write equivalent forms for exponential and logarithmic equations.
Use the definitions of exponential and logarithmic functions to solve equations.

2. Rules and Properties Equivalent Exponential and Logarithmic Forms
10.2 Logarithmic Functions
Rules and Properties
Equivalent Exponential and Logarithmic Forms
For any positive base b, where b  1:
bx = y if and only if x = logb y.
Exponential form
Logarithmic form

3. Example 1 a) Write 27 = 128 in logarithmic form. log2 128 = 7
6.3 Logarithmic Functions
Example 1
a) Write 27 = 128 in logarithmic form.
log2 128 = 7
b) Write log = 4 in exponential form.
64 = 1296

4. Example 2 a. Solve x = log2 8 for x. 2x = 8 x = 3 b. logx 25 = 2
6.3 Logarithmic Functions
Example 2
a. Solve x = log2 8 for x.
2x = 8
x = 3
b. logx 25 = 2
x2 = 25
x = 5

5. Practice c. Solve log2 x = 4 for x. 24 = x x = 16
6.3 Logarithmic Functions
Practice
c. Solve log2 x = 4 for x.
24 = x
x = 16

6. 6.3 Logarithmic Functions
Example 3
a. Solve 10x = for x. Round your answer to the nearest tenth.
log = x
x = 1.161

7. Rules and Properties One-to-One Property of Exponential Functions
6.3 Logarithmic Functions
Rules and Properties
One-to-One Property of Exponential Functions
If bx = by, then x = y.

8. Example 4 Find the value of the variable in each equation:
6.3 Logarithmic Functions
Example 4
Find the value of the variable in each equation:
a) log2 1 = r
b) log7 D= 3
2r = 1
73 = D
20 = 1
D = 343
r = 0

9. Practice Find the value of the variable in each equation:
6.3 Logarithmic Functions
Practice
Find the value of the variable in each equation:
1) log4 64 = v
2) logv 25 = 2
3) 6 = log3 v