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Question Number 210855 by zhou0429 last updated on 20/Aug/24

Answered by Frix last updated on 20/Aug/24

$$x,y>0\wedge x\ne y$$$$x\ln x=y\ln y$$$$\mathrm{Let}y=px\wedge p>0\wedge p\ne 1$$$$x\ln x=px\ln px$$$$\ln x=p\ln p+p\ln x$$$$(1-p)\ln x=p\ln p$$$$\frac{\ln x}{\ln p}=\frac{p}{1-p}$$$${\ln }_{p}x=\frac{p}{1-p}$$$$x=p^{\frac{p}{1-p}}$$$$y=p^{\frac{1}{1-p}}$$

Commented by zhou0429 last updated on 20/Aug/24

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Answered by zhou0429 last updated on 20/Aug/24

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Answered by zhou0429 last updated on 20/Aug/24

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