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Question Number 115711 by DeepakMahato last updated on 27/Sep/20

$$Findthevalueof\mathbf{x}:-$$$${\mathit{x}}^{\mathit{x}}=\mathit{\pi }$$

Answered by MJS_new last updated on 27/Sep/20

$$x\approx 1.85410596792$$

Answered by Dwaipayan Shikari last updated on 27/Sep/20

$${\mathrm{x}}^{\mathrm{x}}=\pi$$$$\mathrm{xlogx}=\log \left(\pi \right)$$$${\mathrm{logxe}}^{\mathrm{logx}}=\log \left(\pi \right)$$$$\mathrm{logx}={\mathrm{W}}_0\left(\log \left(\pi \right)\right)$$$$\mathrm{x}={\mathrm{e}}^{{\mathrm{W}}_0\left(\log \left(\pi \right)\right)}=1.8541..$$

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