About This Chapter
Who's it for?
Anyone who needs help learning or mastering college preparatory math material will benefit from taking this course. You will be able to grasp the subject matter faster, retain critical knowledge longer and earn better grades. You're in the right place if you:
- Have fallen behind in understanding how to solve exponential and logarithmic equations.
- Need an efficient way to learn about logarithms and exponential equations.
- Learn best with engaging auditory and visual tools.
- Struggle with learning disabilities or learning differences, including autism and ADHD.
- Experience difficulty understanding your teachers.
- Missed class time and need to catch up.
- Can't access extra math learning resources at school.
How it works:
- Start at the beginning, or identify the topics that you need help with.
- Watch and learn from fun videos, reviewing as needed.
- Refer to the video transcripts to reinforce your learning.
- Test your understanding of each lesson with short quizzes.
- Submit questions to one of our instructors for personalized support if you need extra help.
- Verify you're ready by completing the Logarithms and Exponential Equations 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 Logarithms and Exponential Equations chapter exam to be prepared.
- Get Extra Support: Ask our subject-matter experts any relevant question. They're here to help!
- Study With Flexibility: Watch videos on any web-ready device.
Students will review:
In this chapter, you'll learn the answers to questions including:
- What are the definitions for an exponential function and a logarithm?
- How do exponential decay and growth differ?
- What are the properties of a logarithm?
- How do I solve exponential and logarithmic equations?
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 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. 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.
6. 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!
7. 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.
8. 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.
9. 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.
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Other chapters within the College Preparatory Mathematics: Help and Review course
- Math Foundations: Help and Review
- Problem Solving & Reasoning Skills
- Percents in Math Basics
- Decimals & Fractions Overview
- Understanding Fractions & Mixed Numbers
- Linear Equations: Help and Review
- Solving and Graphing Inequalities: Help and Review
- Graphing and Factoring Quadratic Equations: Help and Review
- Complex and Imaginary Numbers: Help and Review
- Properties of Exponents: Help and Review
- Properties of Polynomial Functions: Help and Review
- Simplifying and Solving Rational Expressions: Help and Review
- Properties of Functions: Help and Review
- Data & Estimation
- Logic in Math: Help and Review
- Sets: Help and Review
- Basic Probability and Statistics: Help and Review
- Geometric Laws & Proofs
- Geometry in College Preparatory Math: Help and Review
- Grade Level Math Vocabulary: Help and Review
- MTEL Middle School Math/Science: History of Geometry
- MTEL Middle School Math/Science: Geometric Properties & Theorems
- MTEL Middle School Math/Science: Principles of Geometry
- MTEL Middle School Math/Science: Algebraic Applications in Geometry
- MTEL Middle School Math/Science: Using Trigonometric Functions
- MTEL Middle School Math/Science: Trigonometric Identities
- MTEL Middle School Math/Science: Trigonometric Applications