About This Chapter
Logarithmic & Exponential Operations - Chapter Summary
Our instructors define what a logarithm is and the properties associated with logarithms in this helpful chapter. You'll learn about writing logarithmic function inverses and the differences between the shifted graphs and basic graphs of logarithmic functions. Fun lessons outline the definition of an exponential function and how to use rational exponents to simplify expressions. Other topics include the exponential growth as it compares to decay. Once you review this chapter, you will be ready to:
- Add and subtract logarithms
- Use shortcuts to write and estimate logarithms
- Define the logarithmic scale
- Change a rational exponent to a radical exponent and back
- Solve exponential equations
Even the most challenging topics are made simple with the short video lessons provided here. Take your time as you move through the chapter, and re-watch any sections as needed using the video tabs feature. Contact our instructors if you need help with the subjects as you read the chapter. Feel free to access these study materials at any time on any mobile phone, computer or tablet for flexible learning.
1. 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!
2. 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.
3. Adding & Subtracting Logarithms
Logarithms are a fascinating subject in mathematics. They take on many beautiful patterns; two of these happen when we are adding and subtracting logarithms. Let's explore these patterns and deepen our understanding of logarithms in general.
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. 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.
6. 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.
7. Logarithmic Scale: Definition & Overview
A logarithmic scale is a useful way to represent information on a graph, especially when there are exponential changes in the magnitude of the numbers. Learn more, look at several examples and take a quiz to test your knowledge.
8. 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!
9. Rational Exponents
In this video, learn how to go from a rational exponent to a radical expression and back. No tricks or magic, just good math! We'll review the basics and look at a few examples.
10. Simplifying Expressions with Rational Exponents
Simplifying expressions with rational exponents is so easy. In fact, you already know how to do it! We simply use the exponent properties but with fractions as the exponent!
11. 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.
12. 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!
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Other chapters within the Alberta Education Diploma - Mathematics 30-2: Exam Prep & Study Guide course
- Problem Solving with Logic & Reasoning
- Number Systems & Factoring
- Set Theory & Venn Diagrams
- Probability & Uncertainty
- Permutations & Combinations in Probability
- Introduction to Relations & Functions
- Rational Expressions & Quadratic Equations
- Solving Problems with Polynomial Functions
- Sinusoidal Functions
- Alberta Education Diploma - Mathematics 30-2 Flashcards