Question Number 5762 by sanusihammed last updated on 26/May/16
$${Find}\:{the}\:{value}\:{of}\:{x}\: \\ $$$$ \\ $$$$\sqrt{{x}^{{x}^{{x}} } }\:\:=\:\:\mathrm{729} \\ $$$$ \\ $$$${Please}\:{show}\:{me}\:{workings}. \\ $$
Commented by FilupSmith last updated on 27/May/16
$${x}^{{x}^{{x}} } =\mathrm{729}^{\mathrm{2}} \\ $$$${x}^{{x}} \mathrm{ln}{x}=\mathrm{2ln729} \\ $$$${x}\mathrm{ln}{x}+\mathrm{ln}\left(\mathrm{ln}{x}\right)=\mathrm{ln}\left(\mathrm{2ln729}\right) \\ $$$$…? \\ $$