Algebra II: 1001 Practice Problems For Dummies (+ Free Online Practice). Mary Jane Sterling

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Chapter 9

      Exponential and Logarithmic Functions

      Exponential functions are inverses of logarithmic functions — and vice versa. Working with exponential and logarithmic functions requires facility with the correspondence and interrelationship between them. The base of an exponential function must be positive; many mathematicians also exclude the number 1 from being a base. A logarithmic function can have any positive base except the number 1, and the argument (input value) of a logarithmic function must also be positive.

The Problems You’ll Work On

      In this chapter, you’ll work with exponential and logarithmic functions in the following ways:

       Evaluating exponential and logarithmic expressions

       Using the laws of logarithms

       Sketching exponential and logarithmic functions

       Solving for the function’s inverse

       Solving exponential equations

       Solving logarithmic equations and checking for extraneous roots

What to Watch Out For

      Don’t let common mistakes trip you up; remember the following ones when working with exponential and logarithmic functions:

       Not using the order of operations properly when evaluating exponential expressions

       Writing a binomial argument (input statement) incorrectly — splitting it up

       Using laws of logarithms incorrectly

Evaluating Exponential Functions for Input

       481–490 Evaluate the exponential functions for the input values indicated.

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Evaluating Exponential Functions in Base e

       491–500 Evaluate the exponential functions for the input values indicated. Write your answer as a non-negative power of e.

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Sketching the Graphs of Exponential Functions

       501–505 Sketch the graph of the exponential function.

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Finding Values of Logarithmic Expressions for Given Input

       506–515 Evaluate the logarithm.

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