Math Gold Medalist

Lor

2022 AMC 12B 

Problem 16

Suppose $x$ and $y$ are positive real numbers such that\[x^y=2^{64}\text{ and }(\log_2{x})^{\log_2{y}}=2^{7}.\]What is the greatest possible value of $\log_2{y}$?

$\textbf{(A) }3 \qquad \textbf{(B) }4 \qquad \textbf{(C) }3+\sqrt{2} \qquad \textbf{(D) }4+\sqrt{3} \qquad \textbf{(E) }7$

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   Solution