x^{log y - log z} cdot y^{log z - log x} cdot | vedclass

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(C) Let $E = x^{\log y - \log z} \cdot y^{\log z - \log x} \cdot z^{\log x - \log y}$.Taking the logarithm on both sides (assuming base $10$ or any ba

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$1$

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(C) Let $E = x^{\log y - \log z} \cdot y^{\log z - \log x} \cdot z^{\log x - \log y}$.Taking the logarithm on both sides (assuming base $10$ or any base $a$):$\log E = (\log y - \log z) \log x + (\log z - \log x) \log y + (\log x - \log y) \log z$.Expanding the terms:$\log E = (\log y \cdot \log x - \log z \cdot \log x) + (\log z \cdot \log y - \log x \cdot \log y) + (\log x \cdot \log z - \log y \cdot \log z)$.Canceling the terms:$\log E = \log y \log x - \log z \log x + \log z \log y - \log x \log y + \log x \log z - \log y \log z = 0$.Since $\log E = 0$,it implies $E = 10^0 = 1$.

$x^{\log y - \log z} \cdot y^{\log z - \log x} \cdot z^{\log x - \log y} = ?$

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