1. Chapter 3 Exponential and Logarithmic Functions 1

2. 3.4 Solving Exponential and Logarithmic Equations Objectives:  Solve simple exponential and logarithmic equations.  Solve more complicated exponential equations.  Solve more complicated logarithmic equations.  Use exponential and logarithmic equations to model and solve real-life problems. 2

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

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: 4

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? 5

6. Properties of Logarithms 6

7. Properties of Natural Logs 7

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

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. 9

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

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

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

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