If-3-4-2-x-81-2-6-then-x-2-5-

Question Number 146355 by bemath last updated on 13/Jul/21

If 3^{4^{2^{x}}} = 81^{2^{6}} then \sqrt{x^{2} + 5} = ?

Answered by iloveisrael last updated on 13/Jul/21

\Leftrightarrow 3^{4^{2^{x}}} = 81^{2^{6}}

\Leftrightarrow 3^{4^{2^{x}}} = 3^{4 . 2^{6}}

\Leftrightarrow 4^{2^{x}} = 4 . 2^{6} = 4 . 4^{3}

\Rightarrow 4^{2^{x}} = 4^{4}

\Rightarrow 2^{x} = 4; x = 2

\Leftrightarrow \sqrt{x^{2} + 5} = \sqrt{4 + 5} = 3