Question Number 193618 by Brianodhiambo last updated on 17/Jun/23
$${x}^{{log}_{\mathrm{2}} {x}} =\mathrm{256} \\ $$
Answered by aba last updated on 17/Jun/23
$$\mathrm{x}^{\mathrm{log}_{\mathrm{2}} \left(\mathrm{x}\right)} =\mathrm{256}\:\Rightarrow\:\mathrm{x}^{\mathrm{log}_{\mathrm{2}} \left(\mathrm{x}\right)} =\mathrm{2}^{\mathrm{8}} \\ $$$$\Rightarrow\mathrm{log}_{\mathrm{2}} ^{\mathrm{2}} \mathrm{x}=\mathrm{log}_{\mathrm{2}} \mathrm{2}^{\mathrm{8}} \:\Rightarrow\:\mathrm{log}_{\mathrm{2}} ^{\mathrm{2}} \mathrm{x}=\mathrm{8}\:\Rightarrow\:\mathrm{log}_{\mathrm{2}} \mathrm{x}=\pm\mathrm{2}\sqrt{\mathrm{2}} \\ $$$$\Rightarrow\:\mathrm{x}=\mathrm{2}^{\pm\mathrm{2}\sqrt{\mathrm{2}}} \:\checkmark \\ $$