The Dude has a built-in standard syslog server, which can be turned on in the Server settings Syslog tab. It is also possible to change from the default 514 port, to some other TCP port. The Syslog works very well with the RouterOS Remote logging ability.
The Syslog settings allows to set up rules based on source address and log line content. This allows you to filter the incoming logs, and send specific ones to specific log files, or ignore certain logs.
The syslog also allows you to use the standard Dude Notifications for specific incoming logs.
Once you have enabled the Syslog server, the logs will appear in the logfile called "Syslog". You can open the file for viewing in the left side pane.
You can also configure auto-splitting of the log file: