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Question Number 207986 by Thomaseinstein last updated on 02/Jun/24

$${(x-3)}^{\sqrt{x-3}}=3$$

Answered by Frix last updated on 02/Jun/24

$$x-3>0$$$$\sqrt{x-3}\ln (x-3)=3$$$$x=3+{\mathrm{e}}^{2t}$$$$2t\ln t=\ln 3$$$$t{\mathrm{e}}^t=\frac{\ln 3}{2}$$$$t=\mathrm{W}\left(\frac{\ln 3}{2}\right)$$$$x=3+{\mathrm{e}}^{2\mathrm{W}\left(\frac{\ln 3}{2}\right)}\approx 5.12479938302$$

Commented by Thomaseinstein last updated on 05/Jun/24

$$thisonehmm$$

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