If log _{a}(a b)=x, then log _{b}(a b) is | vedclass

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

Question

(D) Given $\log _{a}(a b)=x$.Using the property $\log(mn) = \log m + \log n$,we have:$\log _{a} a + \log _{a} b = x$Since $\log _{a} a = 1$,we get:$1

Vedclass · Accepted Answer

$\frac{x}{x-1}$

Vedclass · Answer

(D) Given $\log _{a}(a b)=x$.Using the property $\log(mn) = \log m + \log n$,we have:$\log _{a} a + \log _{a} b = x$Since $\log _{a} a = 1$,we get:$1 + \log _{a} b = x \Rightarrow \log _{a} b = x - 1$.Now,we need to find $\log _{b}(a b)$:$\log _{b}(a b) = \log _{b} a + \log _{b} b = \log _{b} a + 1$.Using the change of base property $\log _{b} a = \frac{1}{\log _{a} b}$,we substitute the value:$= \frac{1}{x - 1} + 1 = \frac{1 + (x - 1)}{x - 1} = \frac{x}{x - 1}$.

If $\log _{a}(a b)=x,$ then $\log _{b}(a b)$ is

Similar Questions

If $\log _{10} 87.5 = 1.9421$,then the number of digits in $(875)^{10}$ is

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

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

Evaluate: $2 \log _{3} 7 - 7 \log _{3} 2$

If $\log _{10} 2 = 0.3010$ and $\log _{10} 7 = 0.8451,$ then the value of $\log _{10} 2.8$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module