About This Chapter
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- Students who have fallen behind in understanding how to evaluate exponential and logarithmic functions
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- Students who need an efficient way to learn about evaluating exponential and logarithmic functions
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- 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 Evaluating Exponential 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 Evaluating Exponential and Logarithmic Functions chapter exam to be prepared.
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Students will review:
In this chapter, you'll find the answers to questions including:
- What are exponential functions?
- What is the difference between exponential growth and decay?
- What is a logarithm?
- How do I graph logarithms?
- How do I evaluate logarithms?
- What are some basic logarithmic properties?
- How do I solve exponential equations?
- How do I solve logarithmic equations?
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!
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!
3. 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!
4. 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.
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.
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.
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!
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.
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.
10. Power Series: Formula & Examples
A power series gives us what we call an infinite polynomial on our variable x and can be used to define a wide variety of functions. Learn the definition of power series as well as several examples of functions that can be described by them.
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Other chapters within the Precalculus: Help and Review course
- Functions in Precalculus: Help and Review
- Inequalities in Precalculus: Help and Review
- Foundations and Linear Equations in Precalculus: Help and Review
- Graphing and Rational Equations: Help and Review
- Factoring and Graphing Quadratic Equations: Help and Review
- Exponents and Polynomials in Precalculus: Help and Review
- Piecewise and Composite Functions: Help and Review
- Geometry and Trigonometry: Help and Review
- Using Scientific Calculators: Help and Review
- Trigonometry: Help and Review