MLE for the tail index of large losses

Operational losses above a known floor x_m = \1\text{M}$are modeled as Pareto with unknown tail index$\alpha$, density

$f(x \mid \alpha) = \frac{\alpha\, x_m^{\alpha}}{x^{\alpha+1}}, \qquad x \ge x_m.$

A sample of $n = 100$ excess losses has $\sum_i \ln(x_i / x_m) = 40$.

Derive the maximum likelihood estimator of $\alpha$ and compute it.