Double Integrals · Superchallenge problem

Let $D$ be the unit disk $x^2 + y^2 \le 1$. Evaluate $\displaystyle\iint_D \ln\!\big((x - 2)^2 + y^2\big)\,dA$. You may use the fact that $\displaystyle\int_0^{2\pi}\ln\!\big(1 - 2\rho\cos\theta + \rho^2\big)\,d\theta = 0$ for $0 \le \rho < 1$. Give an exact answer.