Question

If $5^{x+1}={25}^{x-2}$; then the value of : $3^{x-3}\times 2^{3-x}$ is $2\frac{1}{m}$.
Value of $m$ is

Answer 1

$5^{x+1}={25}^{x-2}$
$5^{x+1}=5^{2x-4}$
As base is same, equating the powers, we get
$\therefore x+1=2x-4$
$\therefore x=5$
Now, $3^{x-3}\times 2^{3-x}$
$=3^{5-3}\times 2^{3-5}$
$=3^2\times 2^{-2}$
$=\frac{9}{4}$
$=2\frac{1}{4}$