I was under the impression there is no logfile in M2TW but while poking around I found a file in the \logs directory named: "online_mp_31-01-07_21-41.txt" which appears to be a logfile.

This must be a log of the last battle I played today, so at least there appears to be a log created of the last battle played. Dunno if this is old news or helpful to anyone but thought I'd mention it.