Pareto tail index for file sizes

File sizes above a known minimum $x_m$ 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 $n = 50$ files has $\sum_i \ln(x_i / x_m) = 25$.

Estimate the tail index $\alpha$.