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Question Number 172349 by Mikenice last updated on 25/Jun/22

Answered by mr W last updated on 26/Jun/22

$$\log 3\times (\log 3+\log x)=\log 4\times (\log 4+\log y)$$$$\log 4\times \log x=\log 3\times \log y$$$$letX=\log x,Y=\log y$$$$a=\log 3,b=\log 4$$$$\Rightarrow a(a+X)=b(b+Y)$$$$\Rightarrow bX=aY$$$$\Rightarrow X=-a\Rightarrow \log x=-\log 3\Rightarrow x=\frac{1}{3}$$$$\Rightarrow Y=-b\Rightarrow \log y=-\log 4\Rightarrow y=\frac{1}{4}$$

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