College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 6 - Section 6.4 - Logarithmic Functions - 6.4 Assess Your Understanding - Page 449: 42


domain: $(0, +\infty)$

Work Step by Step

RECALL: The logarithmic function $f(x) = \log_a{x}$ is defined only when $x \gt 0$. Thus, its domain is $x \gt 0$. This means that the function $f(x) = \log_5{(x^3)}$ is defined only when $x^3 \gt 0$. Note that the value of $x^3$ will be greater than zero only when $x$ is positive. This means that the given function is defined only when $x\gt0$. Thus, the domain of the given function is $x\gt 0$. In interval notation, the domain is $(0, +\infty)$.
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