Chapter 4, Exponential and Logarithmic Functions - Section 4.3 - Logarithmic Functions - 4.3 Exercises - Page 389: 78

Domain: $[2, 10)$

We need to find the domain of the given function: $h(x)=\sqrt{x-2}-\log_{5}(10-x)$ We know that we can't take the log of a negative number (or 0), so: $10-x\gt 0$ $10\gt x$ Also, we can't square root a negative: $x-2\geq 0$ $x\geq 2$ Thus overall: $2\leq x\lt 10$ Therefore, the domain is: $[2, 10)$.