MLE of a Pareto Tail Index

Suppose large execution slippage magnitudes are modeled as Pareto with known scale $x_m=1$ and unknown tail index $\alpha$, so the density is $$f(x)=\alpha x^{-\alpha-1}, \qquad x\ge 1.$$ If $n=8$ observations satisfy $$\sum_{i=1}^8 \log X_i = 12,$$ find the MLE of $\alpha$. Then estimate $P(X>10)$ under the fitted model.