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Omni-MATH / Find the smallest positive integer n such that underbrace{2^{2 cdot 2}}_{n}>3^{3^{3^{3}}}. (The notation underbrace{2^{2^{2}}}_{n}, is used to denote a power tower with n2 's. For …

Problem

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problem

Find the smallest positive integer nn such that $\underbrace{2^{2 \cdot 2}}_{n}>3^{3^{3^{3}}}$. (The notation $\underbrace{2^{2^{2}}}_{n}$, is used to denote a power tower with n2n 2 's. For example, $\underbrace{2^{22^{2}}}_{n}$ with n=4n=4 would equal 22222^{2^{2^{2}}}.)
Plain-text mathematical notation (without MathML)
Find the smallest positive integer n such that $\underbrace{2^{2 \cdot 2}}_{n}>3^{3^{3^{3}}}$. (The notation $\underbrace{2^{2^{2}}}_{n}$, is used to denote a power tower with n2 's. For example, $\underbrace{2^{22^{2}}}_{n}$ with n=4 would equal 2^(2^(2²)).)
Original LaTeX notation
Find the smallest positive integer $n$ such that $\underbrace{2^{2 \cdot 2}}_{n}>3^{3^{3^{3}}}$. (The notation $\underbrace{2^{2^{2}}}_{n}$, is used to denote a power tower with $n 2$ 's. For example, $\underbrace{2^{22^{2}}}_{n}$ with $n=4$ would equal $2^{2^{2^{2}}}$.)

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Source and history

task_id
ef1105aa-71f2-5ebb-b01b-0bf5a4a6959b
task_key
test--ef1105aa-71f2-5ebb-b01b-0bf5a4a6959b
task_revision_id
1
config / split
/ test

Official source

initial import