About This Chapter
Who's it for?
Anyone who needs help learning or mastering high school trigonometry material will benefit from taking this course. There is no faster or easier way to learn high school trigonometry. Among those who would benefit are:
- Students who have fallen behind in understanding how to graph exponential and logarithmic functions or solve equations containing these types of expressions
- Students who struggle with learning disabilities or learning differences, including autism and ADHD
- Students who prefer multiple ways of learning math (visual or auditory)
- Students who have missed class time and need to catch up
- Students who need an efficient way to learn about exponential and logarithmic functions
- Students who struggle to understand their teachers
- Students who attend schools without extra math learning resources
How it works:
- Find videos in our course that cover what you need to learn or review.
- Press play and watch the video lesson.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Verify you're ready by completing the Exponential & Logarithmic Functions in Trigonometry chapter exam.
Why it works:
- Study Efficiently: Skip what you know, review what you don't.
- Retain What You Learn: Engaging animations and real-life examples make topics easy to grasp.
- Be Ready on Test Day: Use the Exponential & Logarithmic Functions in Trigonometry chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any exponential and logarithmic functions question. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students will review:
This chapter helps students review the concepts in an exponential and logarithmic functions unit of a standard high school trigonometry course. Topics covered include:
- Exponential growth and decay
- Transformations of exponential functions
- Logarithms and the natural base e
- Inverses of logarithmic functions
- Basic and shifted graphs of logarithmic functions
- Logarithmic properties
- Problem-solving steps for logarithmic equations
- The change-of-base formula
- Problem-solving steps for exponential equations
- Large-scale behaviors 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. 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.
16. Isosceles Trapezoid: Definition, Properties & Formula
This lesson highlights the unique properties of the isosceles trapezoid. We will review certain key vocabulary words and discuss the formula identified with the isosceles trapezoid.
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Other chapters within the High School Trigonometry: Help and Review course
- Real Numbers - Types and Properties: Help and Review
- Working with Linear Equations in Trigonometry: Help and Review
- Working with Inequalities in Trigonometry: Help and Review
- Absolute Value Equations in Trigonometry: Help and Review
- Working with Complex Numbers in Trigonometry: Help and Review
- Systems of Linear Equations in Trigonometry: Help and Review
- Mathematical Modeling in Trigonometry: Help and Review
- Introduction to Quadratics in Trigonometry: Help and Review
- Working with Quadratic Functions in Trigonometry: Help and Review
- Coordinate Geometry Review: Help and Review
- Functions for Trigonometry: Help and Review
- Understanding Function Operations in Trigonometry: Help and Review
- Graph Symmetry in Trigonometry: Help and Review
- Graphing with Functions in Trigonometry: Help and Review
- Basic Polynomial Functions in Trigonometry: Help and Review
- Higher-Degree Polynomial Functions in Trigonometry: Help and Review
- Rational Functions in Trigonometry: Help and Review
- Trig - Rational Expressions & Function Graphs: Help & Review
- Trigonometric Functions: Help and Review
- Geometry in Trigonometry: Help and Review
- Triangle Trigonometry: Help and Review
- Working with Trigonometric Graphs: Help and Review
- Trigonometric Equations: Help and Review
- Working with Trigonometric Identities: Help and Review
- Applications of Trigonometry: Help and Review
- Analytic Geometry & Conic Sections in Trigonometry: Help and Review
- Vectors, Matrices & Determinants in Trigonometry: Help and Review
- Polar Coordinates & Parameterizations: Help and Review
- Circular Arcs, Circles & Angles: Help and Review
- TASC Math: Trigonometry