[tex]f(x)=\log (x-8)[/tex]
For the vertical asymptotes, we set the argument of the logarithm to be zero. Therefore,
[tex]\begin{gathered} x-8=0 \\ x-8+8=0+8 \\ x=8 \\ \text{Vertical asymptotes: x = 8} \end{gathered}[/tex]
The domain of the function can be found below
[tex]\begin{gathered} x-8>0 \\ solve\text{ the inequality to obtain the domain} \\ x>8 \\ solve\text{ for x to obtain the domain: x>8 or interval form :(8, }\infty\text{)} \end{gathered}[/tex]
