Answer
$(-\infty, 2)$
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:
$2-x \gt 0$.
Solve the inequality to obtain:
$2-x \gt 0
\\-x \gt 0-2
\\-x \gt -2
\\(-1)(-x) \lt -2(-1)
\\x \lt 2$
(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 $(-\infty, 2)$.