Hi everyone! Read through the material below, watch the videos, and send your professor your questions.

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.

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