Chapter 4, Exponential and Logarithmic Functions - Section 4.3 - Logarithmic Functions - 4.3 Exercises - Page 389: 77

Domain: $(0,2)$

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: $(0,2)$.