That's what a I do. Then a file called "screenlog.0" will be created. Keep in main that this file grows constantly, so eventually you will have to do some thing about it.
To watch the output in real time: tail -f /path to screenlog.0

To clear logs you dont want to keep enable the clear log file at reboot in 1bash
Then add your file address to "Clear_Logs" file

This is probably the easiest way. I made the clear_logs bash to inhibit the runaway growth; which is very quick in somecases where there is a soft crash constantly occuring. Unless I am troubleshooting a rig; I don't need logs, so I use:

Code:

CLEAR_LOGS_ON_BOOT="YES"

with my rigs.