If a^{x}=b^{y}=c^{z}=d^{w}, then log _{a}(b c | vedclass

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(B) Given $a^{x}=b^{y}=c^{z}=d^{w}$.Let $a^{x}=b^{y}=c^{z}=d^{w}=k$.Then $b=k^{1/y}, c=k^{1/z}, d=k^{1/w}$ and $a=k^{1/x}$.We need to find $\log _{a}(

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$x\left(\frac{1}{y}+\frac{1}{z}+\frac{1}{w}\right)$

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(B) Given $a^{x}=b^{y}=c^{z}=d^{w}$.Let $a^{x}=b^{y}=c^{z}=d^{w}=k$.Then $b=k^{1/y}, c=k^{1/z}, d=k^{1/w}$ and $a=k^{1/x}$.We need to find $\log _{a}(b c d)$.Using the property $\log _{a}(M N P) = \log _{a} M + \log _{a} N + \log _{a} P$,we get:$\log _{a}(b c d) = \log _{a} b + \log _{a} c + \log _{a} d$.Since $b=a^{x/y}, c=a^{x/z}, d=a^{x/w}$,we substitute these values:$\log _{a}(b c d) = \log _{a}(a^{x/y}) + \log _{a}(a^{x/z}) + \log _{a}(a^{x/w})$.Using $\log _{a}(a^{n}) = n$,we get:$\log _{a}(b c d) = \frac{x}{y} + \frac{x}{z} + \frac{x}{w} = x\left(\frac{1}{y} + \frac{1}{z} + \frac{1}{w}\right)$.

If $a^{x}=b^{y}=c^{z}=d^{w},$ then $\log _{a}(b c d)=$

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