If $$\frac{dy}{dx} + \frac{2^x y(2y-1)}{2^x - 1} = 0, x, y > 0, y(1) = 1$$, then $$y(2)$$ is equal to

A

$$2 + \log_2 3$$

B

$$2 + \log_2 2$$

C

$$2 - \log_2 3$$

D

$$2 - \log_{-2} 3$$