In Exercises 79–82, use a graphing utility and the change-of-base property to graph each function. y = log3 x

Key Concepts

Logarithmic Functions

Logarithmic functions are the inverses of exponential functions. The function y = log_b(x) answers the question, 'To what power must the base b be raised to obtain x?' Understanding the properties of logarithms, such as their domain, range, and behavior, is essential for graphing and analyzing these functions.

Change-of-Base Formula

The change-of-base formula allows you to convert logarithms from one base to another, which is particularly useful when using calculators that only compute logarithms in base 10 or base e. The formula is expressed as log_b(x) = log_k(x) / log_k(b), where k is any positive number. This concept is crucial for graphing logarithmic functions with different bases.

Graphing Utilities

Graphing utilities, such as graphing calculators or software, enable users to visualize mathematical functions. They can plot functions, including logarithmic ones, and help in understanding their behavior, such as intercepts, asymptotes, and overall shape. Familiarity with these tools enhances the ability to analyze and interpret the graphs of functions effectively.