Question 14
Find the smallest positive integer $n$ such that $\underbrace{2^{2^{2 \cdots}}}_{n} \gt 3^{3^{3^{3}}}$. (The notation $\underbrace{2^{2^{2 \cdots}}}_{n}$ is used to denote a power tower with $n$ $2$'s. For example, $\underbrace{2^{2^{2^{2}}}}_{n=4}$ would equal $2^{2^{2^{2}}}$.)