#### Answer

Domain: $(0,2)$

#### Work Step by Step

We need to find the domain of the given function:
$h(x)=\ln x+\ln(2-x)$
We know that we can't take the log of a negative number, so:
$x\gt 0$
Also:
$2-x\gt 0$
$x\lt 2$
Thus overall: $0\lt x\lt 2$
Therefore, the domain is: $(0,2)$.