I start with Spotlight, which picks out the individual filenames, and then open them in SubEthaEdit.
Spotlight isn't an issue: it's made to be able to scan the whole computer, so obviously it can do my logs standing on its head. I don't know what SubEthaEdit's absolute ceiling is. For a while I was using it on an 85MB text file (not one of my logs, duh ;)). Got a bit sluggish, but it plugged along.
If you're on That Other Platform I assume there are equivalents for each.