We are given the following logarithmic function
[tex]g(x)=\log _3(x-3)[/tex]
Let us find a few points to graph the function.
[tex]\begin{gathered} g(4)=\log _3(4-3)=\log _3(1)=0 \\ g(6)=\log _3(6-3)=\log _3(3)=1 \\ g(5)=\log _3(5-3)=\log _3(2)=0.6 \\ g(8)=\log _3(8-3)=\log _3(5)=1.5 \\ g(9)=\log _3(9-3)=\log _3(6)=1.63 \end{gathered}[/tex]
Let us sketch the graph
