log-2021-x-x-x-674-find-x-

Question Number 150853 by mathdanisur last updated on 15/Aug/21

\log_{2021} \sqrt{x : \sqrt{x : \sqrt{x : . .}}} = 674

find x = ?

Commented by liberty last updated on 16/Aug/21

\sqrt{\frac{x}{\sqrt{\frac{x}{\sqrt{\frac{x}{\sqrt{\frac{x}{⋮}}}}}}}} = 2021^{674}

\Leftrightarrow \sqrt{\frac{x}{2021^{674}}} = 2021^{674}

\Leftrightarrow \frac{x}{2021^{674}} = 2021^{1348}

\Leftrightarrow x = 2021^{2022}

Commented by mathdanisur last updated on 16/Aug/21

Thank you Ser