About This Chapter
Evaluating Exponential and Logarithmic Functions - Chapter Summary and Learning Objectives
If you're looking to build on your understanding of function notation and composition, this chapter has lessons designed to help you do just that. Instructors can show you the uses of exponential functions and their graphs. You can also find out how to evaluate logarithms and solve equations with the change of base formula. By the end of this chapter, you should be able to do the following:
- Graph logarithms and exponential functions
- Use logarithmic properties to evaluate logs
- Solve exponential and logarithmic equations
|What Is an Exponential Function?||Learn what an exponential function is and get examples of how they're used in real life.|
|Exponential Growth vs. Decay||Define exponential growth and decay and learn how to identify their graphs.|
|What is a Logarithm?||Examine how logarithms can be used to solve exponential functions.|
|How to Graph Logarithms: Transformations and Effects on Domain and Range||Practice graphing logarithm functions. Examine how transformations affect domain and range.|
|How to Evaluate Logarithms||Learn methods for writing, estimating and evaluating logarithms. Use the change of base formula and solve problems with a calculator.|
|Logarithmic Properties||Explore uses of the logarithmic product, quotient and power properties.|
|Practice Problems for Logarithmic Properties||Get practice using the logarithmic properties to expand, condense and evaluate logs.|
|How to Solve Exponential Equations||Examine methods for solving exponential equations with logarithms and the change of base formula.|
|How to Solve Logarithmic Equations||Learn how to solve logarithmic equations with exponentials.|
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.
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