Tweetbot generates very much log entries (debug log?) in Console.app.
What's the source of those logs? I didn't find a Tweetbot log file.
A couple of comments. Your screencap does not show the sidebar which will generally show the path to the log in question (EG "/Library/Logs" etc.). Also when you select the log to view on one of the left-hand columns you can select FILE > REVEAL IN FINDER to show the actual log file itself in Finder.