how to send only audit logs to syslog server

Hi Nandhi , 
To send Logs to remote syslog servers , accomplished by 2 methods : 

1. Syslogng utility which runs over Linux : 
   • in this method you will face some difficulties to filter / or send specific log messages such as your scenario here of "Audit Logs " by Gui. 
   • you can send Audit logs by configuring syslog-ng but this can be done only from CLI , to do that follow this article https://my.f5.com/manage/s/article/K56602501 , it just simple modification using some simple linux commands.
2.  High speed logging ( HSL ) and this run over TMOS : 
   • This method is much pretty you can use filters easly , you can control in your Logs which you aim to send. 
     in This Article ( https://techdocs.f5.com/kb/en-us/products/big-ip_ltm/manuals/product/bigip-external-monitoring-implementations-12-0-0/4.html ) you will know about HSL and how to configure it step by step in GUI.

So first method needs CLI interactions whereas secon method can be done using GUI. 

I hope you find my comment useful ! 🙂