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Question Number 32709 by mondodotto@gmail.com last updated on 31/Mar/18

Answered by MJS last updated on 31/Mar/18

$${\log }_{2}3=\frac{\ln 3}{\ln 2}=\mathrm{p}$$$${\log }_{3}2=\frac{\ln 2}{\ln 3}={\mathrm{p}}^{-1}$$$$2^{p^x}=3^{p^{-x}}$$$$p^x\ln 2=p^{-x}\ln 3$$$$p^{2x}=p$$$$p^{2x-1}=1$$$$(2x-1)\ln p=0$$$$2x-1=0$$$$x=\frac{1}{2}$$

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