Ch 8: Logarithmic & Exponential Operations

About This Chapter

Let us help you refresh your understanding of exponential and logarithmic operations with our informative chapter. You'll learn all you need to know in order to prepare for an exam or study for a class test by reviewing these short video lessons and multiple-choice quizzes.

Logarithmic & Exponential Operations - Chapter Summary

Our instructors define what a logarithm is and the properties associated with logarithms in this helpful chapter. You'll learn about writing logarithmic function inverses and the differences between the shifted graphs and basic graphs of logarithmic functions. Fun lessons outline the definition of an exponential function and how to use rational exponents to simplify expressions. Other topics include the exponential growth as it compares to decay. Once you review this chapter, you will be ready to:

  • Add and subtract logarithms
  • Use shortcuts to write and estimate logarithms
  • Define the logarithmic scale
  • Change a rational exponent to a radical exponent and back
  • Solve exponential equations

Even the most challenging topics are made simple with the short video lessons provided here. Take your time as you move through the chapter, and re-watch any sections as needed using the video tabs feature. Contact our instructors if you need help with the subjects as you read the chapter. Feel free to access these study materials at any time on any mobile phone, computer or tablet for flexible learning.

12 Lessons in Chapter 8: Logarithmic & Exponential Operations
Test your knowledge with a 30-question chapter practice test
What is a Logarithm?

1. 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!

Logarithmic Properties

2. 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.

Adding & Subtracting Logarithms

3. Adding & Subtracting Logarithms

Logarithms are a fascinating subject in mathematics. They take on many beautiful patterns; two of these happen when we are adding and subtracting logarithms. Let's explore these patterns and deepen our understanding of logarithms in general.

How to Evaluate Logarithms

4. 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

5. 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.

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

6. 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 Scale: Definition & Overview

7. Logarithmic Scale: Definition & Overview

A logarithmic scale is a useful way to represent information on a graph, especially when there are exponential changes in the magnitude of the numbers. Learn more, look at several examples and take a quiz to test your knowledge.

What Is an Exponential Function?

8. 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!

Rational Exponents

9. Rational Exponents

In this video, learn how to go from a rational exponent to a radical expression and back. No tricks or magic, just good math! We'll review the basics and look at a few examples.

Simplifying Expressions with Rational Exponents

10. Simplifying Expressions with Rational Exponents

Simplifying expressions with rational exponents is so easy. In fact, you already know how to do it! We simply use the exponent properties but with fractions as the exponent!

How to Solve Exponential Equations

11. 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.

Exponential Growth vs. Decay

12. 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!

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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