Where do I find my application log files?

Your application is deployed to /srv/www/APP_SLUG_NAME. There is a special directory structure, inspired by Capistrano:

$ ls /srv/www/APP
total 8
lrwxrwxrwx 1 deploy root   42 2010-04-08 18:46 current -> /srv/www/APP/releases/20100408184610
drwxrwxrwx 3 deploy root 4096 2010-04-08 18:46 releases
drwxrwxrwx 7 deploy root 4096 2010-04-08 18:46 shared
$ ls /srv/www/APP/shared
total 20
drwxr-xr-x 11 deploy root     4096 2010-04-08 18:46 cached-copy
drwxrwx---  2 deploy www-data 4096 2010-04-08 18:46 config
drwxrwx---  2 deploy www-data 4096 2010-04-08 18:48 log
drwxrwx---  2 deploy www-data 4096 2010-04-08 18:46 pids
drwxrwx---  2 deploy www-data 4096 2010-04-08 18:46 system

By default a log directory will be created in your application's root and will be symlinked to /srv/www/APP/shared/log so that logs are preserved during updates.

So your Rails log files will be in /srv/www/APP/shared/log/production.log for example.

Please not that /srv/www is bind-mounted to /mnt/srv/www so your applications are really on the /mnt partition. The same is true for the apache and mysql log files. Both /var/log/apache2 and /var/log/mysql are bind mounted to /mnt/var/log/.