Upperbound for the series $\sum_{j=1}^\infty\ln^2\left(\frac{a_j}{b_j}\right)$

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I would like to estimate an upperbound for the series $$\sum_{j=1}^\infty\ln^2\left(\frac{a_j}{b_j}\right)$$ where $a_j,b_j$ are real sequences, $\sum_ja_j$ and $\sum_jb_j$ converge.