If frac{log x}{b - c} = frac{log y}{c - a} = | vedclass

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(A) Let $\frac{\log x}{b - c} = \frac{\log y}{c - a} = \frac{\log z}{a - b} = k$. Then $\log x = k(b - c)$,$\log y = k(c - a)$,and $\log z = k(a - b)$

Vedclass · Accepted Answer

$xyz = 1$

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(A) Let $\frac{\log x}{b - c} = \frac{\log y}{c - a} = \frac{\log z}{a - b} = k$. Then $\log x = k(b - c)$,$\log y = k(c - a)$,and $\log z = k(a - b)$. Consider the expression $xyz$. Taking the logarithm,$\log(xyz) = \log x + \log y + \log z$. Substituting the values,$\log(xyz) = k(b - c) + k(c - a) + k(a - b) = k(b - c + c - a + a - b) = k(0) = 0$. Since $\log(xyz) = 0$,it follows that $xyz = 10^0 = 1$.

If $\frac{\log x}{b - c} = \frac{\log y}{c - a} = \frac{\log z}{a - b}$,then which of the following is true?

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