Question

State true or false:

Given : ${\log }_{3}m=x$ and ${\log }_{3}n=y$ .

If $2{\log }_{3}A=5x-3y$ ; then A in terms of $m$ and $n$ is $A=\sqrt{\frac{m^5}{n^3}}$.

• A. True
• B. False

Answer 1

The correct option is A True

${\log }_{3}m=x{\log }_{3}n=y2{\log }_{3}A=5x-3y\text{Substituting for x and y}:=5{\log }_{3}m-3{\log }_{3}n2{\log }_{3}A={\log }_3\frac{m^5}{n^3}{\log }_3{A}^2={\log }_3\frac{m^5}{n^3}\text{Removing log and taking square roots on both sides}A=\sqrt{\frac{m^5}{n^3}}$