Question

If $5^{x+1}={25}^{x-2}$ Find the value of : $3^{x-3}\times 2^{3-x}$.

Answer 1

$5^{x+1}={25}^{x-2}$

$\Rightarrow 5^{x+1}=(5^2{)}^{x-2}$

$\Rightarrow 5^{x+1}=5^{2x-4}$ [If bases are equal, powers are also equal]

$\Rightarrow x+1=2x-4$

$\Rightarrow 2x-x=4+1$

$\Rightarrow x=5$

$\therefore 3^{x-3}\times 2^{3-x}=3^{5-3}\times 2^{3-5}=3^2\times 2^{-2}=9\times \frac{1}{4}=\frac{9}{4}$