# Blistering Bananas

Algebra Level 5

$\displaystyle (\log_2x)^4 + (\log_3y)^4 + (\log_465536) = 8\log_2x \log_3y$

Let $$\displaystyle x,y \in \mathbb{R} \ge 1$$ such that they satisfy the equation above.

Determine the least possible $$\displaystyle N \in \mathbb{N}$$, for which $$\displaystyle \log_Nxy \le 1$$.

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