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2019 AMC 12A Question 12

AMC12 · 2019 AMC 12A

Question 12

Positive real numbers $x \ne 1$ and $y \ne 1$ satisfy $\log_2 x = \log_y 16$ and $xy = 64.$ What is $\left(\log_2 \dfrac{x}{y}\right)^2?$
  1. $\dfrac{25}{2}$
  2. $20$
  3. $\dfrac{45}{2}$
  4. $25$
  5. $32$