$$9 \cdot 81^{2-2x} = 27^{2-x}$$
$$3^2 \cdot (3^4)^{2-2x} = (3^3)^{2-x}$$
$$3^2 \cdot 3^{8-8x} = 3^{6-3x}$$
$$3^{10-8x} = 3^{6-3x}$$
$$10-8x = 6-3x$$
$$-5x = -4$$
$$x = \frac{4}{5}$$
Ответ: $$\frac{4}{5}$$