About This Chapter
Logarithms and Exponential Equations - Chapter Summary and Learning Objectives
Do you need a little help with your math skills? Are you at a complete loss when it comes to exponentials or logarithms? You won't have to worry anymore. We have lessons that cover many aspects related to both of these mathematical topics.
Are exponentials driving you crazy? Take a look at our lessons on this topic. We explain all the basics of exponential functions. See how exponential functions are used in real life, so you can understand the real importance of exponentials. You may also want to learn more about exponential growth and decay, which we also cover in our lessons. See the way exponential growth and decay are used in real life and learn the difference between them. We also cover exponential equations in lessons that will teach you how to solve these equations in a simple and straightforward manner.
What is a logarithm? Don't know the answer? You need to take a look at our lessons that teach you what a logarithm is and why they are useful. Also, check out our coverage of how to evaluate logarithms. If you're itching to know more, we will teach you about logarithmic properties and how to solve logarithmic equations, too. Don't forget that we also provide many practice problems, so you can be sure you understand the concepts you've learned.
Studying logarithms through our engaging video lessons can be accessible and enjoyable. Each lesson is taught by an expert on the subject and edited by an experienced video professional. Thanks for watching!
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 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.
5. 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.
6. 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!
7. 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.
8. 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 Math 102: College Mathematics course
- Math Foundations
- Linear Equations
- Solving and Graphing Inequalities
- Graphing and Factoring Quadratic Equations
- Complex and Imaginary Numbers
- Properties of Exponents
- Properties of Polynomials
- Simplifying and Solving Rational Expressions
- Properties of Functions
- Probability and Statistics
- Studying for Math 102