Answer
Domain: $x\gt4$
x-intercept: $(5,0)$
$x=4$ is the vertical asymptote.
Work Step by Step
$f(x)=\ln(x-4)$
Domain:
$x-4\gt0$
$x\gt4$
x-intercept:
$f(x)=\ln(x-4)=0$
$x-4=e^0$
$x-4=1$
$x=5~~$ So, the x-intercept point is $(5,0)$
$\ln x \to\infty$ when $x\to0^+$. So:
$\ln(x-4) \to\infty$ when $x-4\to0^+$
$\ln(x-4) \to\infty$ when $x\to4^+$
Thus, $x=4$ is the vertical asymptote.
