Pareto tail index for city populations

Populations of cities above a known cutoff $x_m$ are modeled as Pareto with unknown index $\alpha$, density $f(x \mid \alpha) = \dfrac{\alpha x_m^{\alpha}}{x^{\alpha+1}}$ for $x \ge x_m$. A sample of $n = 200$ cities has $\sum_i \ln(x_i / x_m) = 50$.

Estimate $\alpha$ by maximum likelihood.