Answer
$\textbf{The graph of $g$ represents the graph of $f$ moved $2$ units to the right and $1$ unit up}$
Work Step by Step
$f(x)=\log x$ $,$ $g(x)=\log(x-2)+1$
Graph both functions in the same viewing rectangle (The graph is shown below) and describe the relationship of the graph of $g$ to the graph of $f$:
$\textbf{The graph of $g$ represents the graph of $f$ moved $2$ units to the right and $1$ unit up}$