log off
and log outto record one's exit from a computer system. (This action may be recorded, or logged, automatically in the computer's memory.) I closed my files and logged off. What time did you log out?
log someone off
and log someone out[for someone] to cause someone to exit from a computer system. (This exit may be recorded, or logged, automatically in the computer's memory.) Mary had to rush off to an appointment, so I logged her off.