Not the canonical use case, but another way to go.
Longer running simple tasks can be launched in a detached "screen" terminal with logged output. You could even give the log a unique name.
Primarily this method is good for something that will take hours and is invoked over SSH with a need to "check up on" from time to time. In preference to backgrounding and disowning.
screen -dmL time -v ./crackpassword
You get the same output a terminal would get, with the caveat that this is asynchronous. Of course it could be a script. The output may need tweaking.