Mathematics

The key insight is that logarithms are only defined for positive arguments. Since the logarithm's input is $(x-4)$, you need to figure out which values of $x$ make that expression positive. Set up the inequality $(x-4) > 0$ and solve for $x$—this gives you all the $x$-values where the function actually exists.

The key insight is that logarithms are only defined for positive arguments. Since the logarithm's input is $(x-4)$, you need to figure out which values of $x$ make that expression positive. Set up the inequality $(x-4) > 0$ and solve for $x$—this gives you all the $x$-values where the function actually exists.