If log x : 3 = log y : 4 = log z : 5,then zx | vedclass

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

Question

(B) Given that $\frac{\log x}{3} = \frac{\log y}{4} = \frac{\log z}{5} = k$.From this,we can express the logarithms as:$\log x = 3k$,$\log y = 4k$,and

Vedclass · Accepted Answer

$y^2$

Vedclass · Answer

(B) Given that $\frac{\log x}{3} = \frac{\log y}{4} = \frac{\log z}{5} = k$.From this,we can express the logarithms as:$\log x = 3k$,$\log y = 4k$,and $\log z = 5k$.We want to find the value of $zx$. Using the properties of logarithms,we have:$\log(zx) = \log z + \log x$.Substituting the values in terms of $k$:$\log(zx) = 5k + 3k = 8k$.Since $\log y = 4k$,we can write $8k = 2(4k) = 2 \log y$.Using the power rule of logarithms,$2 \log y = \log(y^2)$.Therefore,$\log(zx) = \log(y^2)$,which implies $zx = y^2$.

If $\log x : 3 = \log y : 4 = \log z : 5$,then $zx =$

Similar Questions

If $\frac{\log x}{l+m-2n} = \frac{\log y}{m+n-2l} = \frac{\log z}{n+l-2m}$,find the value of $x^2 y^2 z^2$.

$\log _{5}\left(1+\frac{1}{5}\right)+\log _{5}\left(1+\frac{1}{6}\right)+\log _{5}\left(1+\frac{1}{7}\right)+\cdots+\log _{5} \left(1+\frac{1}{624}\right)$

If $\frac{\log _{2} a}{2}=\frac{\log _{3} b}{3}=\frac{\log _{4} c}{4}$ and $a^{1 / 2} \cdot b^{1 / 3} \cdot c^{1 / 4}=24$,then:

If $\log (x+y) = \log \left( \frac{3x - 3y}{2} \right)$,then $\log x - \log y =$

If $\log 2 = 0.3010$ and $\log 3 = 0.4771,$ then the value of $\log _{5} 512$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module