Question Number 126882 by Mathgreat last updated on 25/Dec/20
$$\boldsymbol{{x}}^{\boldsymbol{{x}}} =\mathrm{3} \\ $$
Answered by Lordose last updated on 25/Dec/20
$$\mathrm{x}^{\mathrm{x}} \:=\:\mathrm{3}\:\left\{\mathrm{x}^{\mathrm{x}} \:=\:\mathrm{e}^{\mathrm{xln}\left(\mathrm{x}\right)} \right\} \\ $$$$\mathrm{ln}\left(\mathrm{x}\right)\mathrm{e}^{\mathrm{ln}\left(\mathrm{x}\right)} \:=\:\mathrm{ln3} \\ $$$$\mathrm{lnx}\:=\:\mathrm{W}\left(\mathrm{ln3}\right) \\ $$$$\mathrm{x}\:=\:\mathrm{e}^{\mathrm{W}\left(\mathrm{ln3}\right)} \\ $$$$\mathrm{W}\left(\mathrm{x}\right)\:=\:\mathrm{productlog}\:\mathrm{function} \\ $$$$ \\ $$