Question

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

If $3^{2x-3}$ is expressed in terms of $m$ as $\frac{m^2}{n}$, then the value of $n$ is

• A. $16$
• B. $27$
• C. $36$
• D. $44$

Answer 1

The correct option is B $27$

${\log }_{3}m=x$ ...(Given)
$\therefore m=3^x$
$3^{2x-3}=(3^x{)}^2\times 3^{-3}=\frac{(3^x{)}^2}{27}=\frac{m^2}{27}$ ...(From 1)