# Ch 6: Big Ideas Math Algebra 2 - Chapter 6: Exponential and Logarithmic Functions

### About This Chapter

## How It Works:

- Find the lesson within this chapter that corresponds to what you're studying in the Exponential and Logarithmic Functions chapter of your textbook.
- Watch fun videos that cover the exponential and logarithmic functions concepts you need to learn or review.
- Complete the quiz after watching each video lesson to test your understanding.
- If you need additional help, rewatch the videos until you've mastered the material, or submit a question for one of our instructors.

## Chapter Topics

You'll learn all of the algebra topics covered in the textbook chapter, including:

- Defining exponential growth and decay
- How to write and graph exponential functions
- Using the natural base e and change of base for logarithms
- What a logarithm is and its properties
- Writing inverse logarithmic functions
- Graphing logarithms
- How to solve logarithmic equations and exponential equations
- Solving logarithmic and exponential inequalities
- Modeling with logarithmic and exponential functions

*Big Ideas Math is a registered trademark of Larson Texts, Inc., which is not affiliated with Study.com.*

### 1. 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!

### 2. Writing & Graphing Exponential Functions

In this lesson, we will explore exponential functions and their properties. Through real world examples and explanation, we will see how to write and graph these types of functions.

### 3. 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.

### 4. 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!

### 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. How to Graph Logarithms: Transformations and Effects on Domain/Range

The graph of a basic logarithm is relatively simple. This lesson will show you how to graph a logarithm and what the transformations will do to the graph as well as their effects on the domain and range of the graph.

### 7. 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.

### 8. 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.

### 9. 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!

### 10. 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.

### 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. 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. How to Solve Logarithmic & Exponential Inequalities

In this lesson, we will explore logarithmic and exponential inequalities while showing how they relate to value calculations. We will show examples of several different types of these inequalities.

### 14. Modeling with Exponential & Logarithmic Functions

This lesson will give a quick review of exponential and logarithmic functions and when to use these functions to model data. Then we will explore the use of graphing calculators in finding exponential and logarithmic functions to model given data.

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### Other Chapters

Other chapters within the Big Ideas Math Algebra 2: Online Textbook Help course

- Big Ideas Math Algebra 2 - Chapter 1: Linear Functions
- Big Ideas Math Algebra 2 - Chapter 2: Quadratic Functions
- Big Ideas Math Algebra 2 - Chapter 3: Quadratic Equations and Complex Numbers
- Big Ideas Math Algebra 2 - Chapter 4: Polynomial Functions
- Big Ideas Math Algebra 2 - Chapter 5: Rational Exponents and Radical Functions
- Big Ideas Math Algebra 2 - Chapter 7: Rational Functions
- Big Ideas Math Algebra 2 - Chapter 8: Sequences and Series
- Big Ideas Math Algebra 2 - Chapter 9: Trigonometric Ratios and Functions
- Big Ideas Math Algebra 2 - Chapter 10: Probability
- Big Ideas Math Algebra 2 - Chapter 11: Data Analysis and Statistics