Topic: Exponential and Logarithmic Functions

Subtopic: Exponential and Logarithmic Equations

**Overview**

Much of the material in this lesson is review from an intermediate algebra course, particularly solving basic exponential or logarithmic equations. Our focus will be to expand on the basic processes, bump up the level of difficulty, and tackle some interesting and challenging equations that integrate several methods of simplifying and solving (e.g. using the properties of logarithms or converting between logarithmic and exponential forms). May your knowledge of these functions grow exponentially ;-)

**Objectives**

By the end of this topic you should know and be prepared to be tested on:

- 4.4.1 Algebraically solve exponential equations including those that require converting into logarithmic form or applying a logarithmic function to both sides
- 4.4.2 Algebraically solve exponential equations that have same base throughout and those that contain different bases
- 4.4.3 Algebraically solve logarithmic equations including those that require converting into exponential form or applying an exponential function to both sides
- 4.4.4 Algebraically solve logarithmic equations that require properties or rules of logarithms to simplify
- 4.4.5 Algebraically solve logarithmic equations that have same base logarithm throughout and those that contain different bases
- 4.4.6 Solve exponential and logarithmic equations graphically
- 4.4.7 Recognize equations that can only be solved graphically (i.e. cannot be solved algebraically)
- 4.4.8 Recognize extraneous solutions to exponential and logarithmic equations and those equations that have no solution

**Terminology**

Define: exponential equation, logarithmic equation