Spot The Mistake?

Solve:

$\displaystyle {\Bigl(\frac{2}{3}\Bigr)} ^{x} = {\Bigl(\frac{3}{2}\Bigr)}^{3}$

$\implies \displaystyle \frac {2^{x}} {3^{x}} = \frac {3^{3}} {2^{3}}$

$\implies \displaystyle{2^{3}}. {2^{x}} ={3^{3}}. {3^{x}}$

$\implies \displaystyle2^{3+x} =3^{3+x}$

Since the exponents (3+x) on both sides are equal,

=> 2 = 3