At x=3 the log is 0 and f(3)=2 and x=2 is an asymptote where f(x) approaches minus infinity. The domain is x>2 and the range of f(x) is minus infinity to plus infinity. If the log expression is log to base 2 of x-2, then f(x)=0 (x intercept) is when x-2=1/4, so x=9/4=2.25 and log=-2. When x=2^n where n is very large f(x)=n because x-2 approaches 2^n. The graph is very steep for 2<x<2.25 when it cuts the x axis then its rise is more gradual.