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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.

481. If

482. If

483. If

484. If

485. If

486. If

487. If

488. If

489. If

490. If

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.

491. If

492. If

493. If

494. If

495. If

496. If

497. If

498. If

499. If

500. If

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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Evaluating Natural Logarithms in Base e

516–525 Evaluate the natural logarithm.

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Sketching the Graphs of Log Functions

526–530 Sketch the graph of the log function.

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Rewriting a Log Function as Its Exponential Inverse

531–535 Find the inverse of the log function.

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Changing Exponential Functions to Logarithmic Inverses

536–540 Find the inverse of the exponential function.

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Solving Exponential Equations

541–550 Solve the exponential equation for x.

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Solving Logarithmic Equations

551–570 Solve the logarithmic equation for x.

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