1. Logarithmic Functions

2. Objectives
Write equivalent forms for exponential and logarithmic equations.
Use the definitions of exponential and logarithmic functions to solve equations.

3. Solve for x.
10x = 1,000
10x =
1,000
10x = 85
To solve, a logarithm is needed.

4. Equivalent Exponential and Logarithmic Forms
For any positive base b, where b ≠ 1: bx = y if and only if x = logby.

5. Exponential Form
Logarithmic Form
103 = 1,000
log101,000 = 3

6. Write in logarithmic form.2.
= 625

7. Write in exponential form
1. log100.1 = -1 2.

8. One-to-One Property of Exponents
If bx = by, then x = y.

9. Find the approximate value of each logarithmic expression.

10. Solve each equation for x. Round to the nearest hundredth.2. 3.

11. Find the value of v in each equation.
1. v = log
2. 2 = log7 v

12. Find the value of v in each equation.3. 4.

13. HOMEWORK
Worksheet