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

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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

Similar Questions

The number of solutions of the equation $\log _{4}(x-1)=\log _{2}(x-3)$ is

The number of roots of the equation $\log(-2x) = 2\log(x+1)$ is:

If $(x^2 \log _x 27) \cdot \log _9 x = x + 4$, then the value of $x$ is

The value of $\{x \in R \mid \log_{10} ((1.6)^{1-x^2} - (0.625)^{6(1+x)}) \in R\}$ is

If $\frac{\log x}{b - c} = \frac{\log y}{c - a} = \frac{\log z}{a - b}$,then which of the following is true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module