Ch 23: AEPA Math: Exponential & Logarithmic Functions

About This Chapter

Review what you know about exponential and logarithmic functions with this chapter prior to taking the Arizona Educator Proficiency Assessments (AEPA) Math examination.

AEPA Math: Exponential and Logarithmic Functions - Chapter Summary

Watch this chapter's educational video lessons to recall the process of working with exponential and logarithmic functions. Re-discover their properties as you also explore the process of using the product property and graphing transformations of a logarithm. In doing so, you can prepare to answer related questions on the AEPA Math examination. Utilize these video lessons for:

  • Graphing exponential functions and providing examples of exponential growth
  • Calculating compound interest
  • Evaluating logarithms and solving exponential functions with logarithms
  • Understanding and applying logarithmic properties
  • Calculating exponential equations and logarithmic equations
  • Graphing logarithms and transforming exponential functions
  • Identifying and using the change-of-base formula

The video lessons in this chapter are taught by professional instructors, who are available to answer your questions on these topics. Use the video tags to re-watch specific parts of the lessons. Written transcripts and self-assessment quizzes are included with each video.

AEPA Math: Exponential and Logarithmic Functions - Chapter Objectives

The material you review in this chapter corresponds to the Patterns, Algebra and Functions section of the AEPA Math examination. This portion of the test amounts to 24% of the overall score. In preparation for adding a mathematics endorsement to your Arizona teaching certificate, you'll need to showcase your ability to comprehend logarithmic and exponential functions. The exam includes 150 multiple-choice questions. You'll be allowed four hours and 15 minutes to complete this computer-based examination.

12 Lessons in Chapter 23: AEPA Math: Exponential & Logarithmic Functions
Test your knowledge with a 30-question chapter practice test
What Is an Exponential Function?

1. What Is an Exponential Function?

Brand new technologies don't always catch on right away because they can be expensive and don't always work as well as they should. But once the price comes down, and they start to work better, it doesn't take very long before it seems like everyone has one. Learn about the numbers behind this, exponential functions!

Exponential Growth vs. Decay

2. Exponential Growth vs. Decay

How is it that it only takes four years for our computer to go from top-of-the-line to almost worthless? Well, it has something to do with what's called exponential decay, which we'll learn about here!

Compounding Interest Formulas: Calculations & Examples

3. Compounding Interest Formulas: Calculations & Examples

Compound interest is a great way to have your money work for you. In this lesson, find out the formula for calculating compound interest and practice using the formula with several examples.

What is a Logarithm?

4. What is a Logarithm?

Logarithms can help you solve exponential functions. In this lesson, you will learn about how to work with and recognize logarithms, and how to use logarithm notation with an example problem about earthquakes!

How to Evaluate Logarithms

5. How to Evaluate Logarithms

Using this lesson, you can get practice evaluating logarithms, as well as learn some of the shortcuts behind writing and estimating them. You can also learn how to use your calculator to evaluate logarithms, and learn about a concept called the change of base theory.

Logarithmic Properties

6. Logarithmic Properties

Along with the change of base property, there are three other logarithmic properties that allow you to manipulate expressions to your advantage. Learn about the product rule, quotient rule and power rule here.

Practice Problems for Logarithmic Properties

7. Practice Problems for Logarithmic Properties

As you get further and further into mathematics, logarithms will appear more and more. It's the point of this lesson to get you used to dealing with them and able to know what to do when you see a whole line of paper full of them!

How to Solve Exponential Equations

8. How to Solve Exponential Equations

Read this lesson to learn the steps you need to take to solve exponential equations. You'll see that it's not too difficult; you just need to make use of one other mathematical operation in order to solve your problems.

How to Solve Logarithmic Equations

9. How to Solve Logarithmic Equations

If you're ever picking out a telescope to see your favorite planet, make sure you do the math first! Learn how to solve the logarithmic equation that will get you the size telescope you want.

How to Graph Logarithms: Transformations and Effects on Domain/Range

10. How to Graph Logarithms: Transformations and Effects on Domain/Range

The graph of a basic logarithm is relatively simple. This lesson will show you how to graph a logarithm and what the transformations will do to the graph as well as their effects on the domain and range of the graph.

Transformation of Exponential Functions: Examples & Summary

11. Transformation of Exponential Functions: Examples & Summary

All exponential functions follow a basic graph. But when you make changes to the function, you will see the graph shift and make changes. Watch this video lesson to learn how to easily identify these changes or transformations.

Using the Change-of-Base Formula for Logarithms: Definition & Example

12. Using the Change-of-Base Formula for Logarithms: Definition & Example

Logarithms have many uses in the real world. But what happens when the calculation uses a base other than the standard base 10? Watch this video to find out how to handle this situation and the formula to use.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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Other Chapters

Other chapters within the AEPA Mathematics (NT304): Practice & Study Guide course