Hi There,
So it's been a while since you posted this and you may have found a solution. But if not, that file gets created on the fly by the web adaptor if it doesn't exist and written to if the user the WA is running under has permissions on the directory / file. Since this is baked into the static Logger class in ESRI.ArcGIS.WebAdaptor.dll and not in a config file you can't change this behaviour. But you can delete the file and remove the appropriate permissions on the directory so it doesn't get recreated (which at 10.2.2 which I'm using seems to be the default as I wanted to enable it.) I haven't seen this documented anywhere so I would assume it's an Esri dev only type feature.
Cheers,
Fraser
Eagle Technology - NZ Esri Distributor