BIG-IP AS3 logs to /var/log/restnoded/restnoded.log using f5-logger from the framework. BIG-IP AS3 supports multiple log levels. The log entries contain a JSON block for easy search & reporting by external tools.

Example log entry

Mon, 25 Dec 2017 08:55:00 GMT - fine: [f5-appsvcs] {"message":"script completed","data":{"kind":"tm:cli:script:runstate","command":"run","name":"f5-appsvcs"}}
Mon, 25 Dec 2017 08:55:00 GMT - severe: [f5-appsvcs] {"message":"declaration failed","data":"01020036:3: The requested node (/appsvcs_test_basic_ltm/ was not found."}

For audit logs in /var/log/audit, no matter your BIG-IP user account name, audit logs show all messages from admin and not the specific user name.