# Ch 28: ACT Math: Exponentials and Logarithms

### About This Chapter

## ACT Math: Exponentials and Logarithms - Chapter Summary

You don't have to love math to excel on your ACT exam. You can master the following algebra topics with the lessons in this chapter that can help you shine on test day:

- Exponential functions
- Logarithms and the natural log
- Abstract algebra
- Logarithmic properties
- Solving logarithmic equations
- Evaluating logarithms
- Solving exponential equations

Beginning with pre-algebra and elementary algebra topics, we guide you in grasping the concept and properties of exponents, building a base for this further study. Watch the video lessons dealing with exponentials and logarithms, to learn the higher math skills necessary for the ACT.

### ACT Math Objectives

Of the 60 multiple-choice questions on the math test, 55% of them deal with algebra topics. The following are some of the essential skill sets:

- Concept of exponents
- Properties of exponents and square roots
- Quadratic formula
- Rational and radical expressions
- Absolute value equations and inequalities
- Quadratic inequalities
- Functions
- Modeling

After watching each short video, you'll want to complete the quiz for immediate feedback. You'll be aware, then, if you need further review in any of the areas. Before you know it, you'll be ready to take your ACT.

If you want to use a calculator on the test, check the ACT student site for approved models. Otherwise, the test booklets have blank spaces for your paper and pencil calculations. You'll have 60 minutes to complete the math portion of the test. Your ACT math results will include an overall score for all 60 questions, in addition to sub-scores for combinations of geometry, algebra and trigonometry.

### 1. 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.

### 2. 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!

### 3. 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.

### 4. 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.

### 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. 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!

### 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.

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### Other Chapters

Other chapters within the ACT Prep: Practice & Study Guide course

- ACT: About the Test
- ACT English: Section Overview
- ACT English: Punctuation
- ACT English: Grammar and Usage
- ACT English: Sentence Structure
- ACT English: Parts of an Essay
- ACT English: Rhetorical Strategy
- ACT English: Organization
- ACT English: Style
- ACT Math: Overview
- ACT Math: Number & Quantity
- ACT Math: Pre-Algebra
- ACT Math: Algebraic Expressions
- ACT Math: Radicals
- ACT Math: Linear Equations
- ACT Math: Functions
- ACT Math: Types of Functions
- ACT Math: Absolute Value
- ACT Math: Matrices
- ACT Math: Inequalities
- ACT Math: Probability, Combinations & Factorial
- ACT Math: Data and Statistics
- ACT Math: Exponents
- ACT Math: Polynomials and Quadratics
- ACT Math: Rational Equations and Expressions
- ACT Math: Sequences
- ACT Math: Complex Numbers
- ACT Math: Coordinate Geometry
- ACT Math: Conic Sections
- ACT Math: Triangles
- ACT Math: Plane Geometry
- ACT Math: Lines and Angles
- ACT Math: Trigonometry
- ACT Science Reasoning: Overview
- ACT Science Reasoning: Fundamentals of Science
- ACT Science Reasoning: Evaluating Models
- ACT Reading: Overview
- ACT Reading: Question Types
- ACT Reading: Understanding Reading Passages
- ACT Reading: Word Meanings and Choice
- ACT Reading: Analyzing Reading Passages
- ACT Reading: Practice
- ACT Writing: Overview
- ACT Writing: Essay Skills
- ACT Writing: Planning and Writing
- ACT Writing: Advanced Writing Skills
- ACT Prep Flashcards