Luxo
If you connect the ASIAIR to your computer via a usb cable you should then be able to browse the ASIAIR for the log files (and other files).
The other way to do it - if you have set up your computer to connect to the ASIAIR - is to use Finder/Windows Explorer to browse the files on the ASIAIR. This method is called connecting to the Samba server on the ASIAIR.
To connect to a Samba server, open your client's file manager, and enter the path \SERVER_IP\SHARE_NAME in the address bar, or use smb://SERVER_IP/SHARE_NAME on Linux or macOS, then provide the necessary username and password when prompted to access the shared files.
The SERVER_IP in this case is just the IP address of the ASIAIR. By default, I think this is 10.0.0.1 when you are directly connecting your computer to the WiFI of the ASIAIR.
A point to note here: you might come across a problem connecting if you're using Windows 11. This is because of changes Microsoft made to Windows 11 in 24H2. Use the process in this post on Cloudy Night's to see if it works for you: https://www.cloudynights.com/topic/788291-problem-cant-open-asiair-drive-over-network/page-2#entry14221822
None of the steps I outlined above requires having an Internet connection in order to access the log files of the ASIAIR to your computer. It only requires you being able to connect your computer to the ASIAIR.
