# Ch 7: Exponential Functions & Logarithmic Equations

### About This Chapter

## Exponential Functions & Logarithmic Equations - Chapter Summary

These fun lessons explain what exponential function and logarithm equations are. Additionally, you'll learn about evaluating logarithms and steps for writing the inverse of a logarithmic function. Other topics covered in this chapter include using the correct change-of-base formula when a logarithmic function contains a base other than the standard 10.

Lessons also introduce you to the real-life applications and importance of knowing how to solve exponential equations. After you watch the video lessons in this chapter, you should be ready to:

- Use and graph natural base
*e* - Identify basic graphs and shifted graphs of logarithmic functions
- Solve logarithmic equations
- Utilize equations to calculate exponential growth and rate

Our professional instructors created these video lessons to help make learning as easy and accessible as possible. Watch all the video lessons in the chapter to prepare for a test or exam, or watch only those videos that you know you need to study further. You can take the lesson quizzes to ensure you've understood the material and see where you need to go back and review. Rather than watch an entire video over again, use the video tabs feature to skip ahead to the selected section.

### 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. 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.

### 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. 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. 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.

### 8. 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.

### 9. 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.

### 10. 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.

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### Other Chapters

Other chapters within the BITSAT Exam - Math: Study Guide & Test Prep course

- Expressions & Reasoning in Math
- Complex Numbers & Polynomials in Algebra
- Introduction to Quadratics
- Working with Quadratic Functions Overview
- Mathematical Sequences & Series Overview
- Series & Sequences Application
- Binomial Theorem Overview
- Overview of Matrices & Determinants
- Sets & Relations in Math
- Introduction to Trigonometric Functions
- Trigonometric Identities Overview
- Real World Trigonometric Applications
- Operating with Functions
- Solving Inequalities
- Two-Dimensional Coordinate Geometry
- Straight Lines & Angles in Coordinate Geometry
- Circular Arc & Circles in Coordinate Geometry
- Conic Sections in Coordinate Geometry
- Three-Dimensional Coordinate Geometry
- Limits & Continuity in Differential Calculus
- Calculating Derivatives
- Differentiable Functions & Min-Max Problems
- Differentiability in Integral Calculus
- Overview of Probability in Calculus
- Vectors & Scalars in Math
- Dispersion & Frequency Distributions in Statistics
- Linear Programming & Systems of Equations
- Definite Integrals
- Permutation & Combination
- Mathematical Modeling Overview
- BITSAT Exam - Math Flashcards