CAT 2017 [slot 2] Question with solution 25

It is given that $9^{x-\frac{1}{2}}-2^{2x-2}=4^{x}-3^{2x-3}$

Let us try to reduce them to powers of $3$ and $2$
The given equation can be reduced to $3^{2x-1} + 3^{2x-3} = 2^{2x} + 2^{2x-2}$

Hence, $3^{2x-3} \times 10 = 2^{2x-2} \times 5$
Therefore, $3^{2x-3} = 2^{2x-3}$

This is possible only if $2x-3=0$ or $x=3/2$