what is the domain of this logarithmic function?

Explanation:

Step1: Recall domain of log functions

The domain of a logarithmic function $y = \log_a(x)$ is $x>0$. For a transformed log - function, we consider the argument of the log to be positive. Looking at the graph, the vertical asymptote is at $x=- 2$.

Step2: Determine domain from graph

The function is defined for all $x$ values to the right of the vertical asymptote. So the domain is all real numbers $x$ such that $x > - 2$.

Answer:

$x>-2$ or $(-2,\infty)$