ASM Signature Download logs to Remote SIEM server.

I can't think of an easy way to send just one (or a small number) of log messages off to a log host.

It's possible to use the alertd process to watch for specific log messages and then take an action if a log message is seen, either sending an SNMP trap, email, lcd alarm or executing an external script. You could write a filter for alertd that matches your signature update event log, and then runs an external script that sends a syslog formatted message to your SIEM server. The relevant solution is below:

http://support.f5.com/kb/en-us/solutions/public/14000/300/sol14397.html?sr=32641837