# 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.