WBJEE · Maths · Basic of Mathematics
If \(\left(\log _{5} x\right)\left(\log _{x} 3 x\right)\left(\log _{3 x} y\right)=\log _{x} x^{3},\) then \(y\) equals
- A 125
- B 25
- C \(5 / 3\)
- D 243
Answer & Solution
Correct Answer
(A) 125
Step-by-step Solution
Detailed explanation
We have, \(\begin{aligned} & \log _{5} x \cdot \log _{x} 3 x \cdot \log _{3 x} y=\log _{x} x^{3} \\ \Rightarrow & \frac{\log x}{\log 5} \times \frac{\log 3 x}{\log x} \times \frac{\log y}{\log 3 x}=3 \log _{x} x \end{aligned}\)…
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