I see the system log is getting really big, it was about 6GB today. In the system log I see this:
Does anyone know what it means and how I can solve this?
It is about your cron job issue. you also get these entries in your database. Check your CRON table. This is CRON notification.
You can disable log from admin
Yes , You can rename logfile to keep it for your backup. And create same named log file for fresh logs to be kept for your magento system. The notification will get resolved.