About This Chapter
How it works:
- Begin your assignment or other high school trigonometry 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 High School Trigonometry 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 exponential growth and decay, natural base functions, logarithmic properties, the change-of-base formula 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 high school trigonometry
- Don't have access to their math teacher outside of class
Why it works:
- Engaging Tutors: We make learning about 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 trigonometry tutor, these video lessons are thoroughly reviewed.
- Convenient: Imagine a tutor as portable as your laptop, tablet or smartphone. Learn about exponential and logarithmic functions on the go!
- Learn at Your Pace: You can pause and re-watch lessons as often as you'd like, until you master the material.
- Define and graph an exponential function.
- Compare decay with exponential growth.
- Learn how to utilize the natural base e.
- Identify transformations of exponential functions.
- Define and evaluate logarithms.
- Explore logarithmic and inverse functions.
- Work with exponentials and logarithms.
- Define and provide examples of basic and shifted graphs.
- Identify the properties of logarithms.
- Solve logarithmic and exponential equations.
- Explain how the change-of-base formula is used.
- Solve the population growth formula.
- Identify exponential and logarithmic functions according to the behavior of graphs.
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. Transformation of Exponential Functions: Examples & Summary
All exponential functions follow a basic graph. But when you make changes to the function, you will see the graph shift and make changes. Watch this video lesson to learn how to easily identify these changes or transformations.
4. Using the Natural Base e: Definition & Overview
In this video lesson, you will learn what kind of number 'e' is. Also learn the formal name for this unique number. See what kind of graph the natural base 'e' graphs into, as well as the uses of these types of functions.
5. 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!
6. 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.
7. Writing the Inverse of Logarithmic Functions
Watch this video lesson to learn how inverses are related to the original function. Also learn a method to find the inverse of logarithmic functions that you can easily use.
8. Exponentials, Logarithms & the Natural Log
Use the properties of exponentials and logarithms to learn how carbon dating works. This lesson covers properties of a natural log and rules of logarithms.
9. Basic Graphs & Shifted Graphs of Logarithmic Functions: Definition & Examples
Watch this video lesson and you will see what the basic graph of the logarithmic function looks like. You will also be able to identify the kind of shifts that will occur by just looking at a logarithmic function when you finish the video.
10. 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.
11. 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!
12. 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.
13. Using the Change-of-Base Formula for Logarithms: Definition & Example
Logarithms have many uses in the real world. But what happens when the calculation uses a base other than the standard base 10? Watch this video to find out how to handle this situation and the formula to use.
14. 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.
15. Calculating Rate and Exponential Growth: The Population Dynamics Problem
You know how the world population keeps increasing? It's increasing faster now than it was 100 or 1,000 years ago. In this lesson, learn how differential equations predict this type of exponential growth.
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Other chapters within the High School Trigonometry: Tutoring Solution course
- Real Numbers - Types and Properties: Tutoring Solution
- Working with Linear Equations in Trigonometry: Tutoring Solution
- Working with Inequalities in Trigonometry: Tutoring Solution
- Absolute Value Equations in Trigonometry: Tutoring Solution
- Working with Complex Numbers in Trigonometry: Tutoring Solution
- Systems of Linear Equations in Trigonometry: Tutoring Solution
- Mathematical Modeling in Trigonometry: Tutoring Solution
- Introduction to Quadratics in Trigonometry: Tutoring Solution
- Working with Quadratic Functions in Trigonometry: Tutoring Solution
- Coordinate Geometry Review: Tutoring Solution
- Functions for Trigonometry: Tutoring Solution
- Understanding Function Operations in Trigonometry: Tutoring Solution
- Graph Symmetry in Trigonometry: Tutoring Solution
- Graphing with Functions in Trigonometry: Tutoring Solution
- Basic Polynomial Functions in Trigonometry: Tutoring Solution
- Higher-Degree Polynomial Functions in Trigonometry: Tutoring Solution
- Rational Functions in Trigonometry: Tutoring Solution
- Rational Expressions & Function Graphs in Trigonometry: Tutoring Solution
- Trigonometric Functions: Tutoring Solution
- Geometry in Trigonometry: Tutoring Solution
- Triangle Trigonometry: Tutoring Solution
- Working with Trigonometric Graphs: Tutoring Solution
- Trigonometric Equations: Tutoring Solution
- Working with Trigonometric Identities: Tutoring Solution
- Applications of Trigonometry: Tutoring Solution
- Analytic Geometry & Conic Sections in Trigonometry: Tutoring Solution
- Vectors, Matrices & Determinants in Trigonometry: Tutoring Solution
- Polar Coordinates & Parameterizations: Tutoring Solution
- Circular Arcs, Circles & Angles: Tutoring Solution