Hi,
I'm not sure what logs you are talking about.
There should be no problem with getting TCP connection Built/Teardown messages to the Syslog server whatever their used TCP port is.
If on the otherhand you are trying to get some specific data about that HTTPS connection I think you need either a module for the ASA or an addiotional device/service to handle going through HTTPS traffic for you.
The "inspect http" configuration doesnt apply to https traffic. You also can't see anything related to the HTTPS traffic with the ASA alone since its encrypted.
- Jouni