I saw the transfers.log file and it's empty. My guess is that logging is turned off.
I did some research. If you mean /var/log/pure-ftpd/transfer.log I don't see anything. I went to make sure that reporting is turned on but I don't see the syslog directory...
I'm reading http://download.pureftpd.org/pub/pure-ftpd/doc/README
Log messages are sent to the syslog daemon. You can disable logging with
If you want all FTP messages to be redirected to a file, say /var/log/ftp,
add this line to your /etc/syslog.conf file:
Where is there a different syslog in Ubuntu 10.04?