1.6 Exponential and Logarithm Functions



The exponential and logarithmic functions are inverse functions of each other. Exploring this relationship between them, we discuss properties of the exponential and logarithm functions, including their graphs and the rules for manipulating exponents and logs. We define the important number e that is the base for the natural logarithm, and is the standard base that we use for exponential functions in calculus. The exponential function turns out to be very useful in certain kinds of population madeling.

By the end of your studying, you should know:

On-screen applet instructions: There is a show-and-hide button for the natural log function. How are ex and ln(x) related?


The ground noise created by an airplane taking off at time t = 0 is measured in decibels, and is given by

where t is measured in seconds. How long will it be before the level of noise drops to 2 decibels?

Find the inverse of

and find the domains of f and f–1.

Find all solutions to the equation ln(x + 4) = 2ln(x) – ln(2).


Comparing Exponential Functions


See short videos of worked problems for this section.


Take a quiz.


See Exercises for 1.6 Exponential and Logarithm Functions (PDF).

Work online to solve the exercises for this section, or for any other section of the textbook.

Interesting Application

World record times for the mile-- are they exponential?

1.5 Trigonometric Functions Table of Contents 1.7 Case Study: Modeling with Elementary Functions

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Copyright © 2005 Donald L. Kreider, C. Dwight Lahr, Susan J. Diesel