Logging the request coming to a Virtual Server

It does not log hits by default. You need an iRule for that. Attach this to your virtual server. This will log to syslog.

when CLIENT_ACCEPTED {
  log local0. "Client [IP::client_addr] accessed [virtual]"
}

But high speed logging is what you need for production. Define a pool with log server(s) in it.

when CLIENT_ACCEPTED {
  set hsl [HSL::open -proto UDP -pool syslog_server_pool]
  HSL::send $static::hsl "<190> Client [IP::client_addr] accessed [virtual]\n"
}