The syslog.service seems to be empty and there is no configuration file like syslog.conf or rsyslog.conf. So, how can we go about using syslog in an application running on the beagleboard?
If you are running Angstrom and systemd, then syslog has been replaced with the journal (see /var/log/README). Your application writes to the journal using the syslog api.
The journal is coming to Debian and Ubuntu along with systemd.