Lesson 14: Properties of Exponential and Logarithmic Functions

Topic: This lesson covers Chapter 14 in the book, Exponential and Logarithmic Functions.

WeBWorK: There are three WeBWorK assignments on today’s material: Logarithmic Functions - Properties, Logarithmic Functions - Equations, and Exponential Functions - Equations

Today’s goal is to review the properties/rules of exponents and logs, and then see how we can use them to solve equations.

#### Lesson Notes (Notability – pdf):

This .pdf file contains most of the work from the videos in this lesson. It is provided for your reference.

## Properties of Exponential and Logarithmic Functions

You should already be familiar with the rules of exponents and rules of logarithms. I realize you may not remember them, so read through the material below and take a look at the examples in the first video.

#### Review: Properties of Exponential Functions

The following rules apply to exponential functions (where and are any real numbers):   #### Review: Properties of Logarithmic Functions

The following rules apply to logarithmic functions (where and , and is an integer).   Change of base formula (if : Example 14.1: Combine the terms using the properties of logarithms so as to write as one logarithm.

a) b) c) d) Example 14.2:  Write the expressions in terms of elementary logarithms  and, in part also Assume that a) b) c) ## Solving Exponential and Log Equations

Now we’re going to use these properties to solve equations.

Example 14.5: Solve for .

a) b) c) d) e) f) g) h) Example 14.6: Solving Log Equations

a) b) c) d) e) f) That’s it for today, everybody! Give the WeBWorK a try.