About This Chapter
Exponentials and Logarithms
Exponentials and logarithms are exact opposite operations. Exponentials deal with multiplying, whereas logarithms help you find unknown exponents. You have likely seen exponentials and logarithms before when working with algebraic equations. Remember the small numbers placed to the upper right side of a number? Those small numbers, called exponents, are used when dealing with exponentials and logarithms.
In these algebra video lessons, you'll learn the basic definitions of exponentials and logarithms. You'll study concepts, such as exponential function and how to evaluate logarithms, also referred to as logs. Through real-life examples, you'll learn how to apply these concepts to everyday life, so you can be sure you understand them completely. Another concept learned in the video lessons is exponential growth and decay. This concept allows you to discover how exponentials are used to predict growth or negative growth in future situations.
Not only will you learn what these concepts are and how they can be applied to real life situations, but you will be taught how to solve such equations. You'll be walked through equations to learn exactly how to apply what you learn to any equation you may come across. Along the way, the lessons will explore logarithmic properties and other topics.
While algebra may not be easy for everyone, these video lessons break down the concepts and present them in a way that will make it easy for you to remember how to work with exponentials and logarithms. You'll discover concepts that will aid you in solving such equations and allow you to firmly understand what these concepts are and how they are dealt with in algebra.
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.
9. Practice Problem Set for Exponentials and Logarithms
If you'd like more opportunities to practice the concepts you've learned in this chapter, please download the following practice problem set. After you've completed the set, you can download the answer key to check your work and help your understanding. Please note that these documents are not permissible for use during your proctored exam.
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Other chapters within the Math 101: College Algebra course
- Foundations of Linear Equations
- Matrices and Absolute Value
- Factoring with FOIL, Graphing Parabolas and Solving Quadratics
- Complex Numbers
- Exponents and Polynomials
- Rational Expressions
- Radical Expressions & Functions
- Probability Mechanics
- Sequences and Series
- Studying for Math 101