About This Chapter
How it works:
- Begin your assignment or other precalculus work.
- Identify the exponential and logarithmic functions concepts that you're stuck on.
- Find fun videos on the topics you need to understand.
- Press play, watch and learn!
- Complete the quizzes to test your understanding.
- As needed, submit a question to one of our instructors for personalized support.
Who's it for?
This chapter of our Precalculus Tutoring Solution will benefit any student who is trying to learn about exponential and logarithmic functions to earn better grades. This resource can help students, including those who:
- Struggle with understanding logarithmic properties, exponential equations, transformations or any other exponential and logarithmic functions topic
- Have limited time for studying
- Want a cost effective way to supplement their math learning
- Prefer learning math visually
- Find themselves failing or close to failing their exponential and logarithmic functions unit
- Cope with ADD or ADHD
- Want to get ahead in precalculus
- Don't have access to their math teacher outside of class
Why it works:
- Engaging Tutors: We make learning exponential and logarithmic functions simple and fun.
- Cost Efficient: For less than 20% of the cost of a private tutor, you'll have unlimited access 24/7.
- Consistent High Quality: Unlike a live precalculus tutor, these video lessons are thoroughly reviewed.
- Convenient: Imagine a tutor as portable as your laptop, tablet or smartphone. Learn exponential and logarithmic functions on the go!
- Learn at Your Pace: You can pause and rewatch lessons as often as you'd like, until you master the material.
- Define exponential functions.
- Compare and contrast exponential growth and decay.
- Translate graphs of exponential functions both horizontally and vertically.
- Graph functions that use the natural base e.
- Define and evaluate logarithms.
- Write logarithmic equations in exponential form and write the inverse of these functions.
- Graph logarithmic functions and learn how to identify the vertical asymptote, domain and range.
- List logarithmic properties.
- Solve logarithmic equations.
- Evaluate logarithmic expressions using the change-of-base formula.
- Solve exponential equations.
- Calculate rate and exponential growth.
- Compare the behavior of exponential and logarithmic functions.
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 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.
5. 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.
6. 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.
7. 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!
8. 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.
9. 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 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 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 Precalculus: Tutoring Solution course
- Functions: Tutoring Solution
- Inequalities: Tutoring Solution
- Foundations and Linear Equations: Tutoring Solution
- Graphing and Rational Equations: Tutoring Solution
- Factoring and Graphing Quadratic Equations: Tutoring Solution
- Exponents and Polynomials: Tutoring Solution
- Piecewise and Composite Functions: Tutoring Solution
- Geometry and Trigonometry: Tutoring Solution
- Using Scientific Calculators: Tutoring Solution
- Trigonometry: Tutoring Solution