2. Let $N=2^{\left(2^{2}\right)}$ and $x$ be a real number such that $N N^{\left(N^{N}\right)}=2^{\left(2^{x}\right)}$. Find $x$.
Answer:
66
We compute
$$
N^{\left(N^{N}\right)}=16^{16^{16}}=2^{4 \cdot 2^{4 \cdot 2^{4}}}=2^{2^{2^{6}+2}}=2^{2^{66}},
$$
so $x=66$.