2016 AMC 12A Problem 16

The graphs of y=\log_3 x, y=\log_x 3, y=\log_\frac{1}{3} x, and y=\log_x \dfrac{1}{3} are plotted on the same set of axes. How many points in the plane with positive x-coordinates lie on two or more of the graphs?

\textbf{(A)}\ 2\qquad\textbf{(B)}\ 3\qquad\textbf{(C)}\ 4\qquad\textbf{(D)}\ 5\qquad\textbf{(E)}\ 6

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.