Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 9 - Section 9.3 - Logarithmic Functions - Exercise Set - Page 700: 50


$(-\infty, 7)$

Work Step by Step

RECALL: The domain of the logarithmic function $f(x) = \log_a{x}$ is $x \gt 0$. Thus, the domain of the given function is the set of all real numbers such that: $7-x \gt 0$. Solve the inequality to obtain: $7-x \gt 0 \\-x \gt 0-7 \\-x \gt -7 \\(-1)(-x) \lt -7(-1) \\x \lt 7$ (Note that the inequality sign flips when we multiply by a negative number on both sides of the inequality.) Therefore, the domain of the given function is $(-\infty, 7)$.
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