See graph and explanations.
Work Step by Step
Step 1. Graph the function $y=log_3(x-1), x\gt1$; as the inequality includes an equal sign, make the boundary solid. Step 2. Using a test point away from the boundary, such as $(4,0)$, we have $0\gt log_33=1$ which is not true; thus the other side without this test point should be shaded as shown in the figure.