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Question Number 48155 by gunawan last updated on 20/Nov/18

$${\left(\sqrt{2}\right)}^x={\left(\sqrt{3}\right)}^y$$$$x\ne 0$$$$y\ne 0$$$$\mathrm{find}x,y$$

Answered by MJS last updated on 20/Nov/18

$$x\ln \sqrt{2}=y\ln \sqrt{3}$$$$y=x\frac{\ln \sqrt{3}}{\ln \sqrt{2}}=x\frac{\ln 3}{\ln 2}\Rightarrow \mathrm{infinite}\mathrm{number}\mathrm{of}\mathrm{solutions}$$

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