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Ch 19: Exponential Functions & Logarithmic Functions: Help and Review

About This Chapter

The exponential functions and logarithmic functions chapter of this Precalculus Help and Review course is the simplest way to master exponential functions and logarithmic functions. This chapter uses simple and fun videos that are about five minutes long, plus lesson quizzes and a chapter exam to ensure students learn the essentials of exponential functions and logarithmic functions.

Who's it for?

Anyone who needs help learning or mastering precalculus material will benefit from taking this course. There is no faster or easier way to learn precalculus. Among those who would benefit are:

  • Students who have fallen behind in understanding how to resolve exponential functions and logarithmic functions
  • Students who struggle with learning disabilities or learning differences, including autism and ADHD
  • Students who prefer multiple ways of learning math (visual or auditory)
  • Students who have missed class time and need to catch up
  • Students who need an efficient way to learn about exponential functions and logarithmic functions
  • Students who struggle to understand their teachers
  • Students who attend schools without extra math learning resources

How it works:

  • Find videos in our course that cover what you need to learn or review.
  • Press play and watch the video lesson.
  • Refer to the video transcripts to reinforce your learning.
  • Test your understanding of each lesson with short quizzes.
  • Verify you're ready by completing the Exponential Functions and Logarithmic Functions chapter exam.

Why it works:

  • Study Efficiently: Skip what you know, review what you don't.
  • Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
  • Be Ready on Test Day: Use the Exponential Functions and Logarithmic Functions chapter exam to be prepared.
  • Get Extra Support: Ask our subject-matter experts any exponential functions and logarithmic functions question. They're here to help!
  • Study With Flexibility: Watch videos on any web-ready device.

Students will review:

In this chapter, you'll learn the answers to questions including:

  • What is the definition of an exponential function?
  • What is the difference between exponential growth and decay?
  • What is the definition of a logarithm?
  • How do I graph a logarithm?
  • How do I evaluate a logarithm?
  • How do I solve an exponential equation?
  • What are the steps for calculating rate and exponential growth?
  • What is unique to the large-scale behavior of exponential and logarithmic functions with different bases?

18 Lessons in Chapter 19: Exponential Functions & Logarithmic Functions: Help and Review
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!

Transformation of Exponential Functions: Examples & Summary

3. 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 Natural Base e: Definition & Overview

4. Using the Natural Base e: Definition & Overview

In this video lesson, you will learn what kind of number 'e' is. Also learn the formal name for this unique number. See what kind of graph the natural base 'e' graphs into, as well as the uses of these types of functions.

What is a Logarithm?

5. 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

6. 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.

Writing the Inverse of Logarithmic Functions

7. Writing the Inverse of Logarithmic Functions

Watch this video lesson to learn how inverses are related to the original function. Also learn a method to find the inverse of logarithmic functions that you can easily use.

Exponentials, Logarithms & the Natural Log

8. Exponentials, Logarithms & the Natural Log

Use the properties of exponentials and logarithms to learn how carbon dating works. This lesson covers properties of a natural log and rules of logarithms.

Basic Graphs & Shifted Graphs of Logarithmic Functions: Definition & Examples

9. Basic Graphs & Shifted Graphs of Logarithmic Functions: Definition & Examples

Watch this video lesson and you will see what the basic graph of the logarithmic function looks like. You will also be able to identify the kind of shifts that will occur by just looking at a logarithmic function when you finish the video.

Logarithmic Properties

10. 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

11. 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 Logarithmic Equations

12. 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.

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

13. 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.

How to Solve Exponential Equations

14. 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.

Calculating Rate and Exponential Growth: The Population Dynamics Problem

15. Calculating Rate and Exponential Growth: The Population Dynamics Problem

You know how the world population keeps increasing? It's increasing faster now than it was 100 or 1,000 years ago. In this lesson, learn how differential equations predict this type of exponential growth.

Behavior of Exponential and Logarithmic Functions

16. Behavior of Exponential and Logarithmic Functions

After watching this video lesson, you will be able to recognize exponential and logarithmic functions by looking at the end behavior of the graphs. You will also learn how the graphs change.

Continuous Functions: Properties & Definition

17. Continuous Functions: Properties & Definition

In this lesson, you will learn what a continuous function is and how to identify one by tracing your finger or pencil on a graph or by using three properties of continuous functions.

Power Rule for Derivatives: Examples & Explanation

18. Power Rule for Derivatives: Examples & Explanation

The power rule for derivatives is simply a quick and easy rule that helps you find the derivative of certain kinds of functions. In this lesson, you will learn the rule and view a variety of examples.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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