There is no way in the UI per se.
Well other than Admin panel -> Settings -> System
Lower the time set for Purge Logs.
If you are comfortable with SQL then you can go to the DB and directly remove them with a query.
This will delete any logs older then 30 days.
DELETE FROM ost_syslog WHERE DATEDIFF(NOW(),created) > 30
This will delete all logs
TRUNCATE TABLE ost_syslog
Make sure that you back up your database BEFORE you run any SQL commands directly on your database just to be safe.