If (log _{5} x)(log _{x} 3x)(log _{3x} y) = l | vedclass

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(A) Given equation: $(\log _{5} x)(\log _{x} 3x)(\log _{3x} y) = \log _{x} x^{3}$ Using the change of base formula $\log _{b} a = \frac{\log a}{\log b

Vedclass · Accepted Answer

$125$

Vedclass · Answer

(A) Given equation: $(\log _{5} x)(\log _{x} 3x)(\log _{3x} y) = \log _{x} x^{3}$ Using the change of base formula $\log _{b} a = \frac{\log a}{\log b}$, we get: $\frac{\log x}{\log 5} 	imes \frac{\log 3x}{\log x} 	imes \frac{\log y}{\log 3x} = 3 \log _{x} x$ Simplifying the left side by cancelling common terms: $\frac{\log y}{\log 5} = 3(1)$ $\log _{5} y = 3$ Converting to exponential form: $y = 5^{3} = 125$

If $(\log _{5} x)(\log _{x} 3x)(\log _{3x} y) = \log _{x} x^{3}$, then $y$ equals

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