Answer
$(0,\infty)$
Work Step by Step
We are given the function:
$$g(x)=\log_3 x+6.$$
The logarithmic function is defined when its argument is strictly positive, therefore we have:
$$\begin{align*}
x>0.
\end{align*}$$
So the domain of the function $g$ is:
$$(0,\infty).$$