As the author says this is pretty common in machine learning circles. I used the same trick in POPFile for text classification because you end up dealing with tiny probabilities, but manageable negative log probabilities. And clearly division is just subtraction, just as multiplication becomes addition.
What amused me at the time was that this is how people used to do multiplication with a slide rule or log table. Funny how old ideas come back.
Heh, I'm just old enough to have learned the log table method in high school Algebra II; that was right after scientific calculators hit $90 in 2010 dollars (http://en.wikipedia.org/wiki/TI-30 at $25 then) but of course the books hadn't caught up yet. And the trick is indeed very useful.