I need to switch from database logging to syslog
This article explains the whole process into details.

The very bottom line is activating the Syslog module (a core module), and configure it on admin/settings/logging/syslog. It should already work out-of-the-box.

To make sure you can find the log file, you can set it in /etc/syslog.conf and /etc/rsyslog.d/50-default.conf.