> Take the log of all terms (allowed, because log keeps the sum monotonic) It seems you're employing a + b < c <=> log(a) + log(b) < log(c), which doesn't hold

> Take the log of all terms (allowed, because log keeps the sum monotonic) It seems you're employing a + b < c <=> log(a) + log(b) < log(c), which doesn't hold (consider 10, 10, and 20). (the real rule is a * b < c <=> log(a) + log(b) < log(c)), because log(a) + log(b) <=> log(a * b)