Chapter 4, Exponential and Logarithmic Functions - Section 4.3 - Logarithmic Functions - 4.3 Exercises - Page 388: 74

Domain: $(-\infty,\ 4)$

We need to find the domain of the given function: $f(x)=\log_{5}(8-2x)$ We know that we can't take the log of a negative number, so: $8-2x\gt 0$ $8\gt 2x$ $4\gt x$ Thus the domain is: $(-\infty,\ 4)$