There is no logfile for uploads/downloads.

PS: Some more background information on gnutella. Only gnutella searching is anonymous, downloading/uploading is not... this is P2P, peer to peer: While you download/upload stuff your IP is stored in the TCP/IP header... other gnutella servants have a upload logfile (e.g. Bearshare), so at least those users can see what is downloaded by whom (IP) and when.
PPS: Downloading MP3s is not illegal in my country (yet), but think about supporting your favourit artists by buying their CDs,