AMC 12B 2022 Problem 16

Suppose x and y are positive real numbers such that

x^{y}=2^{64} \text { and }\left(\log _{2} x\right)^{\log _{2} y}=2^{7}

What is the greatest possible value of \log _{2} y ?

Answer Choices
A. 3
B. 4
C. 3+\sqrt{2}
D. 4+\sqrt{3}
E. 7