Question Number 171820 by Mikenice last updated on 21/Jun/22
$${solve}\:{for}\:{x}: \\ $$$${x}^{{x}} =\mathrm{2}^{\mathrm{2048}} \\ $$
Commented by mr W last updated on 21/Jun/22
$${x}^{{x}} =\mathrm{2}^{\mathrm{2048}} =\mathrm{2}^{\mathrm{8}×\mathrm{256}} =\mathrm{256}^{\mathrm{256}} \\ $$$$\Rightarrow{x}=\mathrm{256} \\ $$