Question about iRule or other methods for remote logging

There are a lot of ways to accomplish this. A simple search for iRule Logging will return an easy afternoon or two worth of reading. I would caution you about logging too much, especially to the BigIP. The BigIP was never intended to be a log aggregator and is optimized for high speed traffic processing. You can quickly overwhelm the CPU by trying to log too much of the traffic being processed.

Here is an example of an irule to use the High Speed Logging mechanism to log data to a remote server: https://devcentral.f5.com/codeshare/logging-irule-1180