There's an alternate approach that I was mentally contrasting with. You tend to see it with e.g. Ruby apps on Heroku: you can't "log into" a live app, but you can launch an IRB REPL—with all the app's dependencies loaded—in the context of the live app.
Having this ability to "futz around in prod" frequently obviates the need for prescient levels of logging. You can poke at the problem until it crashes for you.
Ruby folks, don't let not being in Heroku stop you from taking this approach, because it's the best. pry-remote (are you using irb instead of pry? please stop) will give you the same fantastic behavior. It's part of every persistent Ruby service I deploy (guarded for internal access only, of course, don't be crazy).
Having this ability to "futz around in prod" frequently obviates the need for prescient levels of logging. You can poke at the problem until it crashes for you.