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
If you're planning on putting some money in the bank to save up for that next thing you've got to have, it might be best to know a little about exponential equations first. Learn how to check how long it will take you to have as much money as you need here!
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.
Earning College Credit
Did you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.
To learn more, visit our Earning Credit Page
Transferring credit to the school of your choice
Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.
Other chapters within the Math 101: College Algebra course