There are lots of questions related to this one, but they all start with the (right) assumption that the output isn't logged.
So my question is: where?
Nowhere: Bash's (and any other shell that I know of's) output isn't logged.
Since output is displayed on the screen, it has to be stored somewhere anyway.
It is, but most likely not in plain text and not even on the disk (although this really is up to the terminal emulator): most likely, and at least in most cases, in a memory segment allocated by the terminal emulator.
However for sure it isn't logged to a file, at least not by the shell, and I don't know of terminal emulators which log the output to a file by default.
Indeed this doesn't mean it's impossible to log the terminal output: first I'll mention something that I think not many are aware of, since I've never saw anyone mentioning this at least here on Ask Ubuntu: Konsole allows to save the scrollback to a file (perhaps there are other terminal emulators that provide such a functionality, Konsole is just the only one I know of), although this is limited by Konsole's scrollback size limit.
This is often not really useful though, and most likely you'll want to look into "proper" solutions to log a whole session's output to a file (How do I log all input and output in a terminal session? and Ron's answer).