Answer
Domain: $(0,2)$
Work Step by Step
For a logarithmic function to be defined,
its argument must be POSITIVE,
So, g is defined for
$ x>0\qquad$and$\qquad 2-x>0$
(both terms must be defined)
$\left[\begin{array}{lll}
x>0 & & 2-x>0\\
& & 2>x
\end{array}\right]$
So, x is greater than 0 and less than 2,
Domain: $(0,2)$