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 $\log _{10} 7 = a$,then $\log _{10} \left( \frac{1}{70} \right)$ is equal to

If $\log_{10} 2 = 0.3010$,the number of digits in $2^{64}$ is:

If $a^{x}=b^{y}=c^{z}=d^{w},$ then $\log _{a}(b c d)=$

If $\log _{10} 50+\log _{10} 20=x,$ then $x$ is equal to

Evaluate: $\frac{\log \sqrt{27}+\log \sqrt{1000}+\log 8}{\log 120}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module