There is the /getlog command line switch, but to use that you need the Session ID, which for a completed process you can only get from the DB. A running process can get it's own ID using a calculation, so I guess you could output that somewhere (file or queue) for later use. If you're thinking that's messy, then you'd be right.
Another option is make running processes create a bespoke log in a format/location that suits you better. There are 3rd party tools for this (such as Splunk) or you couls just use another DB.
