## Intermediate Algebra for College Students (7th Edition)

Published by Pearson

# Chapter 9 - Section 9.3 - Logarithmic Functions - Exercise Set: 48

#### Answer

$(-6, +\infty)$.

#### 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: $x+6 \gt 0$. Solve the inequality to obtain: $x + 6 \gt 0 \\x \gt 0-6 \\x \gt -6$ Therefore, the domain of the given function is $(-6, +\infty)$.

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