  We consider the sum of squared logarithms inequality and investigate possible
connections with the theory of majorization. We also discuss alternative
sufficient conditions on two sets of vectors $a,b\in\mathbb{R}_+^n$ so that
$\sum_{i=1}^n(\log a_i)^2\ \leq\ \sum_{i=1}^n(\log b_i)^2\,.\notag $
Generalizations of some inequalities from information theory are obtained,
including a generalized information inequality and a generalized log sum
inequality, which states for $a,b\in\mathbb{R}_+^n$ and $k_1,...,k_n\in
[0,\infty)$: $ \sum_{i=1}^na_i\,\log\prod_{s=1}^m(\frac{a_i}{b_i} + k_s)\ \geq\
\log\prod_{s=1}^m(1+k_s)\,.\notag $
