Question Number 193612 by Noorzai last updated on 17/Jun/23
Answered by aba last updated on 17/Jun/23
$$\mathrm{x}^{\mathrm{x}^{\mathrm{2}} } =\mathrm{3}\:\Rightarrow\:\mathrm{x}^{\mathrm{2}} \mathrm{lnx}=\mathrm{ln3} \\ $$$$\Rightarrow\mathrm{2lnx}.\mathrm{e}^{\mathrm{2lnx}} =\mathrm{2ln3}\:\Rightarrow\:\mathrm{2lnx}=\mathrm{W}\left(\mathrm{2ln3}\right) \\ $$$$\Rightarrow\:\mathrm{x}=\mathrm{e}^{\frac{\mathrm{1}}{\mathrm{2}}\mathrm{W}\left(\mathrm{2ln3}\right)} \approx\:\mathrm{1}.\mathrm{56555} \\ $$