Question

$5^{x+1}={25}^{x-2}$. If the value of $3^{x-3}\times 2^{3-x}$ is $b\frac{1}{4}$ then, $b$ is:

Answer 1

Given equation is $5^{x+1}={25}^{x-2}$
$=>5^{x+1}=5^{2x-4}$
As base are equal, equate the powers,
$=>x+1=2x-4$
$=>x=5$
Now, $3^{x-3}\times 2^{3-x}$
$=3^{5-3}\times 2^{3-5}$
$=3^2\times 2^{-2}$
$=\frac{9}{4}$
$=2\frac{1}{4}$

Hence, $b=2$