Answer
Domain: $(0, +\infty)$
Range: $(-\infty, +\infty)$
Work Step by Step
Recall:
The function $y=\log_a{b}$ has $b\gt0$ so its domain of $(0, +\infty)$ has a range of $(-\infty, +\infty)$.
The given function has $b=x-3$ so its domain is:
\begin{align*}
x-3 &\gt0\\
x&\gt3
\end{align*}
Thus, the function has:
Domain: $(0, +\infty)$
Range: $(-\infty, +\infty)$