1. Copyright © 2014, 2010, 2007 Pearson Education, Inc.
Chapter 4
Exponential and Logarithmic Functions
4.2 Logarithmic Functions
Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1

2. Objectives:
Change from logarithmic to exponential form.
Change from exponential to logarithmic form.
Evaluate logarithms.
Use basic logarithmic properties.
Graph logarithmic functions.
Find the domain of a logarithmic function.
Use common logarithms.
Use natural logarithms.

3. Definition of the Logarithmic Function
For x > 0 and b > 0, b 1,
y = logbx is equivalent to by = x.
The function f(x) = logbx is the logarithmic function with base b.

4. Example: Changing from Logarithmic to Exponential Form
Write each equation in its equivalent exponential form:
means

5. Example: Changing from Exponential to Logarithmic Form
Write each equation in its equivalent logarithmic form:
means

6. Example: Evaluating Logarithms
Evaluate:

7. Basic Logarithmic Properties Involving One
1. logbb = 1 because 1 is the exponent to which b must be raised to obtain b. (b1 = b)
2. logb1 = 0 because 0 is the exponent to which b must be raised to obtain 1. (b0 = 1)

8. Example: Using Properties of Logarithms
Evaluate: log99
Evaluate: log81

9. Inverse Properties of Logarithms
For b > 0 and b 1,

10. Example: Using Inverse Properties of Logarithms
Evaluate:

11. Graphs of Logs

12. Graphs of Logs (cont.)

13. Example: Graphs Logarithmic Functions (continued)
Looking at the graph of , we could just invert each ordered pair to obtain the inverse or logarithmic function:

14. Example: Finding the Domain of a Logarithmic Function
Find the domain of
Think of the graph:

15. Common Logarithms
The logarithmic function with base 10 is called the common logarithmic function.
The function is usually expressed

16. Properties of Common Logarithms

17. Natural Logarithms
The logarithmic function with base e is called the natural logarithmic function.
The function is usually expressed

18. Properties of Natural Logarithms