Question

If $5^{x+1}={25}^{x-2}$; find the value of:

$3^{x-3}\times 2^{3-x}$

Answer 1

$5^{x+1}={25}^{x-2}{5}^{x+1}=(5^2{)}^{x-2}{5}^{x+1}=5^{2x-4}x+1=2x-42x-x=4+1x=53^{x-3}\times 2^{3-x}=3^{5-3}\times 2^{3-5}=3^2\times 2^{-2}=9\times \frac{1}{2^2}=\frac{9}{4}$