Spot The Mistake?

Solve:

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

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

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

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

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

=> 2 = 3