About This Chapter
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- Define exponential functions.
- Compare exponential decay to exponential growth.
- Identify logarithms.
- Go through the logarithm evaluation process.
- Find the properties of logarithms.
- Practice solving equations that address logarithmic properties.
- Explore exponential equations.
- Decipher the steps for solving 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 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 College Algebra: Tutoring Solution course
- Overview of Linear Equations: Tutoring Solution
- Solving Matrices and Absolute Value: Tutoring Solution
- Overview of Inequalities: Tutoring Solution
- Factoring with FOIL, Graphing Parabolas and Solving Quadratics: Tutoring Solution
- Imaginary and Complex Numbers: Tutoring Solution
- Working with Exponents and Polynomials: Tutoring Solution
- Identifying and Working with Functions: Tutoring Solution
- Rational Expressions: Tutoring Solution
- Factorials and Binomial Theorem: Tutoring Solution
- Calculating Sequences and Series: Tutoring Solution