inequality – $sum frac {1} {alpha + log_a {b}} le frac {2}{alpha}$

This is another olympiad-problem my teacher gave us to train.
$$sum frac {1}{alpha + log_a{b}} le frac {2}{alpha}$$ with $alpha in (0, 2)$ and $a, b, c in (0, 1) cup (1, infty)$. After working a little bit with it, we get $$sum log_{a ^ alpha b} {a} le frac {2}{alpha}$$, but I don’t know how to go on.