It should be going to the ReadyAPI log when you actually run the test case.
When you run your script in the Script Assertion Editor, the "log" variable is a Logger that appends to that window. When your assertion runs normally as part of a test case, log will be a logger that writes to the Script Log.
If you really want to write to the Script log while testing your assertion in the Script Assertion editor, you can use:
import org.apache.log4j.Logger
Logger scriptLog = Logger.getLogger("groovy.log")
scriptLog.info "Hello World"
Or of course, just reassign the existing log variable:
import org.apache.log4j.Logger
log = Logger.getLogger("groovy.log")
log.info "Hello World"
Disclaimer: I found the name of the logger ("groovy.log"
) by running log.info log.name
and running the test case. I did this on the Open Source version of SoapUI. It's possible that the logger name is different in ReadyAPI.