Answer
$(-\infty, 4)$
Work Step by Step
RECALL:
The logarithmic function $f(x) = \log_a{x}$ is defined only when $x$ is greater than $0$.
This means that the given function is only defined when $8 - 2x$ is greater than zero.
Thus,
$8-2x \gt 0
\\-2x \gt 0-8
\\-2x \gt -8$
Divide $-2$ to both sides of the inequality.
Note that the inequality symbol will flip too the opposite direction since a negative number was divided to each side.
$x \lt \frac{-8}{-2}
\\x \lt 4$
Therefore, the domain of the given function is $x \lt 4$ In interval notation, the domain is $(-\infty, 4)$.
