Question Number 115711 by DeepakMahato last updated on 27/Sep/20
$${Find}\:{the}\:{value}\:{of}\:\boldsymbol{\mathrm{x}}:- \\ $$$$\boldsymbol{{x}}^{\boldsymbol{{x}}} =\boldsymbol{\pi} \\ $$
Answered by MJS_new last updated on 27/Sep/20
$${x}\approx\mathrm{1}.\mathrm{85410596792} \\ $$
Answered by Dwaipayan Shikari last updated on 27/Sep/20
$$\mathrm{x}^{\mathrm{x}} =\pi \\ $$$$\mathrm{xlogx}=\mathrm{log}\left(\pi\right) \\ $$$$\mathrm{logxe}^{\mathrm{logx}} =\mathrm{log}\left(\pi\right) \\ $$$$\mathrm{logx}=\mathrm{W}_{\mathrm{0}} \left(\mathrm{log}\left(\pi\right)\right) \\ $$$$\mathrm{x}=\mathrm{e}^{\mathrm{W}_{\mathrm{0}} \left(\mathrm{log}\left(\pi\right)\right)} =\mathrm{1}.\mathrm{8541}.. \\ $$