If a^x = b^y = c^z = d^w,then the value of xl | vedclass

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(A) Given,$a^x = b^y = c^z = d^w = k$ (let). Then,$x = \log_a k$,$y = \log_b k$,$z = \log_c k$,$w = \log_d k$. Taking reciprocals,$\frac{1}{x} = \log_

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$\log_a(bcd)$

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(A) Given,$a^x = b^y = c^z = d^w = k$ (let). Then,$x = \log_a k$,$y = \log_b k$,$z = \log_c k$,$w = \log_d k$. Taking reciprocals,$\frac{1}{x} = \log_k a$,$\frac{1}{y} = \log_k b$,$\frac{1}{z} = \log_k c$,$\frac{1}{w} = \log_k d$. We need to evaluate $x\left(\frac{1}{y} + \frac{1}{z} + \frac{1}{w}\right)$. Substituting the values,we get $x\left(\log_k b + \log_k c + \log_k d\right) = x \log_k(bcd)$. Since $x = \log_a k$,the expression becomes $\log_a k \cdot \log_k(bcd)$. Using the change of base formula $\log_a k \cdot \log_k(bcd) = \log_a(bcd)$.

If $a^x = b^y = c^z = d^w$,then the value of $x\left(\frac{1}{y} + \frac{1}{z} + \frac{1}{w}\right)$ is

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