I have seen multiple documents on sending logs to my syslog server,
is this the right document https://support.f5.com/csp/article/K13080
and is this the only step:
Adding a remote syslog server using the Configuration utility
In fact everything depends on the logs that you want to send to your server.
You can use high-speed remote logging.
You can configure the BIG-IP system to log information about BIG-IP system processes and send the log messages to remote high-speed log servers. You can filter the data that the system logs based on alert-level and source.
You can also send some information according to your convenience via an irule:
otherwise you can also send the logs with "Adding a remote syslog server".
but as explained above everything depends on the logs you want to send.