Answer
$(-\infty, 7)$
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 $(-\infty, 7)$.
