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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