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

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(A) Given, $a^x = b^y = c^z = d^w = k$ (let).Taking log with base $a$:$x = y \log_a b = z \log_a c = w \log_a d$.Thus, $\frac{1}{y} = \frac{\log_a b}{

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$\log_a(bcd)$

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(A) Given, $a^x = b^y = c^z = d^w = k$ (let).Taking log with base $a$:$x = y \log_a b = z \log_a c = w \log_a d$.Thus, $\frac{1}{y} = \frac{\log_a b}{x}$, $\frac{1}{z} = \frac{\log_a c}{x}$, and $\frac{1}{w} = \frac{\log_a d}{x}$.Now, $x\left(\frac{1}{y} + \frac{1}{z} + \frac{1}{w}\right) = x\left(\frac{\log_a b}{x} + \frac{\log_a c}{x} + \frac{\log_a d}{x}\right)$.$= x \cdot \frac{1}{x} (\log_a b + \log_a c + \log_a d)$.$= \log_a(bcd)$.

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

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