HMMT February, 2019

Algebra Difficulty 4.6 AIME Prove it United States

Problem:
Let $N=2^{\left(2^{2}\right)}$ and $x$ be a real number such that $N^{\left(N^{N}\right)}=2^{\left(2^{x}\right)}$ . Find $x$ .

Solution

Solution:
We compute
$\text{N (N N ) =16 16 16 =2 4 2 4 2 4 =2 2 2 6 +2 =2 2 66}$
so $x=66$ .

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