About This Chapter
Algebra II: Exponential and Logarithmic Functions - Chapter Summary
There are several ways to review and visually display data, but to do so you need to understand certain mathematical concepts. This chapter provides you with extensive knowledge in using exponential and logarithmic functions to analyze and graph different types of information. As this chapter covers a large number of topics, our instructors have carefully split the chapter into short, manageable lessons. Each lesson looks at one main topic, providing you with a compact but thorough review. As you make your way through the lessons, remember that you can submit your questions directly to our experts from your user dashboard. When you complete this chapter, you will gain the skills needed to:
- Determine the characteristics of an exponential function
- Show exponential decay versus growth
- Establish the definition of a logarithm
- Outline how transformations impact domain/range with graphs
- Figure out how to analyze logarithms
- Inspect logarithmic properties and solve sample problems
- Evaluate procedures for solving logarithmic and exponential equations
- Grasp the specifics of the change of base formula and how to use it
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. Change Of Base Formula: Logarithms & Proof
Logarithmic expressions are frequently written with a base that can not be simplified easily. When this happens, you can use the change of base formula to change the base to something that can be worked with. This lesson will show you how to do that, and give some examples followed by a quiz.
5. 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.
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.
7. 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.
8. 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!
9. 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.
10. 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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Other chapters within the Algebra II: High School course
- Algebra II: Real Numbers
- Algebra II: Complex and Imaginary Numbers Review
- Algebra II: Exponents and Exponential Expressions Review
- Algebra II: Properties of Functions Review
- Algebra II: Linear Equations Review
- Algebra II: Systems of Linear Equations
- Algebra II: Inequalities Review
- Algebra II: Absolute Value Review
- Algebra II: Graphing and Factoring Quadratic Equations Review
- Algebra II: Quadratic Equations
- Algebra II: Factoring
- Algebra II: Polynomials
- Algebra II: Rational Expressions
- Algebra II: Graphing and Functions
- Algebra II: Conic Sections
- Algebra II: Roots and Radical Expressions Review
- Algebra II: Sequences & Series
- Algebra II: Combinatorics
- Algebra II: Calculations, Ratios, Percent & Proportions Review
- Algebra II: Statistics
- Algebra II: Trigonometry
- Teacher Resources for High School Algebra II