# Ch 15: Exponential Functions & Logarithmic Functions

Watch online math video lessons to learn about exponential growth, the natural log, the change-of-base formula and more. These bite-sized lessons help you quickly retain critical info on exponential and logarithmic functions.

## Exponential Functions and Logarithmic Functions - Chapter Summary and Learning Objectives

Did you know that exponential functions and logarithmic functions are inverses of each other? This means that if you can tackle one type of function, you'll likely be able to work with the other. Instructors teaching this chapter go over the ins and outs of both functions by covering such topics as logarithmic properties, Euler's number and the change-of-base formula. They also show you how to graph and solve exponential and logarithmic equations, and explore their uses to calculate exponential growth and decay as well as interest rates. Use this chapter to learn how to:

• Identify graphs of exponential functions
• Write and evaluate logarithmic functions
• Describe logarithmic properties
• Apply the change-of-base formula

Video Objectives
What Is an Exponential Function? Review the types of graphs. Learn what the equation of an exponential function looks like.
Exponential Growth vs. Decay Examine the graphs of exponential growth and exponential decay. Learn how to differentiate between the two.
Transformation of Exponential Functions: Examples, Lesson & Quiz Follow the steps required to translate an exponential function vertically and horizontally. Learn how to graph reversals.
Using the Natural Base e: Definition, Lesson & Quiz Explore characteristics of Euler's number. Find out what the graph of a natural log looks like, and examine its uses.
What Is a Logarithm? Discover the relationship between logarithms and exponential functions.
How to Evaluate Logarithms Review logarithmic form. Explore the uses of the change-of-base formula to evaluate logarithms without whole numbers in the solution.
Writing the Inverse of Logarithmic Functions: Lesson & Quiz Find out how to change logarithmic equations into exponential form and back again.
Exponentials, Logarithms & the Natural Log Examine the rules of the natural log alongside properties of exponentials. Explore some of their real-life applications.
Basic Graphs & Shifted Graphs of Logarithmic Functions: Definition & Examples Understand how to graph a basic logarithmic function and perform transformations that flip or shift graphs vertically and horizontally.
Logarithmic Properties Investigate the product, quotient and power properties of logarithms.
Practice Problems for Logarithmic Properties Practice using logarithmic properties to expand, condense and evaluate logs.
How to Solve Logarithmic Equations Survey the uses of inverse operations, the product property and exponentiating to solve logarithmic equations.
Using the Change-of-Base Formula for Logarithms: Definition & Example Learn how the change-of-base formula can be used to evaluate logarithmic expressions with a base other than ten.
How to Solve Exponential Equations Practice solving exponential equations by using logarithms and the change-of-base formula.
Calculating Rate and Exponential Growth: The Population Dynamics Problem Learn how to write and solve differential equations useful for determining exponential growth.
Comparing the Large-Scale Behavior of Exponential and Logarithmic Functions with Different Bases Examine how growth rates are represented on graphs of exponential and logarithmic functions.

16 Lessons in Chapter 15: Exponential Functions & Logarithmic Functions
Test your knowledge with a 30-question chapter practice test
Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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