About This Chapter
Who's it for?
This unit of our High School Precalculus Homeschool course will benefit any student who is trying to learn to evaluate and solve logarithmic functions. There is no faster or easier way to learn precalculus. Among those who would benefit are:
- Students who require an efficient, self-paced course of study to learn to identify the vertical asymptote, range and domain of a logarithmic function.
- Homeschool parents looking to spend less time preparing lessons and more time teaching.
- Homeschool parents who need a precalculus curriculum that appeals to multiple learning types (visual or auditory).
- Gifted students and students with learning differences.
How it works:
- Students watch a short, fun video lesson that covers a specific unit topic.
- Students and parents can refer to the video transcripts to reinforce learning.
- Short quizzes and an Evaluating Logarithmic Functions unit exam confirm understanding or identify any topics that require review.
Evaluating Logarithmic Functions Unit Objectives:
- Complete practice problems that have logarithmic properties.
- Learn about decay versus exponential growth.
- Vertically and horizontally translate an exponential function.
- Provide examples of basic and shifted graphs.
- Study logarithms, exponentials and the natural log.
- Learn to write the inverse of 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. Behavior of Exponential and Logarithmic Functions
After watching this video lesson, you will be able to recognize exponential and logarithmic functions by looking at the end behavior of the graphs. You will also learn how the graphs change.
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Other chapters within the High School Precalculus: Homeschool Curriculum course
- Graphing Linear Equations: Homeschool Curriculum
- Solving & Graphing Inequalities: Homeschool Curriculum
- Absolute Value Expressions: Homeschool Curriculum
- Graphing Complex Numbers: Homeschool Curriculum
- Solving Linear Systems: Homeschool Curriculum
- Linear Models: Homeschool Curriculum
- Quadratics: Homeschool Curriculum
- Quadratic Functions & Equations: Homeschool Curriculum
- Geometry Basics: Homeschool Curriculum
- Functions for Precalculus: Homeschool Curriculum
- Using Function Operations: Homeschool Curriculum
- Recognizing Graph Symmetry: Homeschool Curriculum
- How to Graph Functions: Homeschool Curriculum
- Rate of Change: Homeschool Curriculum
- Polynomial Functions: Homeschool Curriculum
- Higher-Degree Polynomials: Homeschool Curriculum
- Difference Quotients in Precalculus: Homeschool Curriculum
- Working with Rational Expressions: Homeschool Curriculum
- Functions in Trigonometry: Homeschool Curriculum
- Using Trigonometric Graphs: Homeschool Curriculum
- Trigonometric Equations: Homeschool Curriculum
- Basic Trigonometric Identities: Homeschool Curriculum
- Laws of Sine & Cosine: Homeschool Curriculum
- Graphing Piecewise Functions: Homeschool Curriculum
- Vectors & Matrices: Homeschool Curriculum
- Mathematical Sequences: Homeschool Curriculum
- Identifying Conic Sections: Homeschool Curriculum
- Parametric Equations: Homeschool Curriculum
- Continuity: Homeschool Curriculum
- Limits in Precalculus: Homeschool Curriculum
- Groups & Sets in Algebra: Homeschool Curriculum