1. Chapter 3 Exponential and Logarithmic Functions
Pre-Calculus
Chapter 3
Exponential and Logarithmic Functions

2. 3.3 Properties of Logarithms
Objectives:
Rewrite logarithms with different bases.
Use properties of logarithms to evaluate or rewrite logarithmic expressions.
Use properties of logarithms to expand or condense logarithmic expressions.
Use logarithmic functions to model and solve real-life problems.

3. Change-of-Base Formula
Used to convert a log from one base to another.
To convert from base a to base b:

4. Change-of-Base Formula
Most commonly used to convert a log to base 10 or to natural log for calculator use.
To convert from base a to base 10:
To convert from base a to natural log:

5. Examples
Solve each by converting to common log and then using your calculator.
Solve again by converting to natural log. How do the answers compare?

6. Properties of Logarithms

7. Properties of Natural Logs

8. Examples
Write each logarithm in terms of ln 2 and ln 3.

9. Using the Properties
Properties of logs are used to rewrite logarithmic expressions, specifically to expand or condense them.
Expand – Take a single, complicated log expression and write it as several simple log expressions.
Condense – Take several simple log expressions and write them as one log expression.

10. Examples – Expanding Expressions
Use the properties of logarithms to expand each expression.

11. Examples – Condensing Expressions
Use the properties of logarithms to condense each expression.

12. Additional Examples
Given f (x) = ln x, determine whether each statement below is true or false. Justify your answer.

13. Homework 3.3
Worksheet 3.3
# 5, 11, 15, 23 – 61 odd, 67 – 79 odd, 82, 85 – 91 odd, 103, 105