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Question Number 134110 by mohammad17 last updated on 27/Feb/21

Answered by mr W last updated on 27/Feb/21

$$\log \left(LHS\right)$$$$=\log \frac{y}{z}\times \log x+\log \frac{z}{x}\times \log y+\log \frac{x}{y}\times \log z$$$$=(\log y-\log z)\log x+(\log z-\log x)\log y+(\log x-\log y)\log z$$$$=\log y\log x-\log z\log x+\log z\log y-\log x\log y+\log x\log z-\log y\log z$$$$=0$$$$\Rightarrow LHS=1$$

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