Find domain and vertical asymptote of $LaTeX: \displaystyle f(x) = \ln{\left(x - 1 \right)} - 4$

The base function $LaTeX: \displaystyle \ln(x)$ has vertical asymptote $LaTeX: \displaystyle x =0$ and domain $LaTeX: \displaystyle (0, \infty)$ . $LaTeX: \displaystyle f(x)$ is shifted 1 unit right and 4 units down. This gives the vertical asymptote as $LaTeX: \displaystyle x = 1$ and the domain as $LaTeX: \displaystyle (1, \infty)$