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2016 AMC 12A Question 16

AMC12 · 2016 AMC 12A

Question 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?
  1. $2$
  2. $3$
  3. $4$
  4. $5$
  5. $6$