Unfortunately, Apple does not provide much in the way of log information or details about what is going on with the AirPort routers.
Assuming that you have a recent Mac operating system installed on your Mac.......
Open AirPort Utility (Finder > Applications > Utilities > AirPort Utility)
Hold down the option key on your Mac while you double-click on the picture of the AirPort Extreme
A list of current Wireless Clients is displayed. Click on the small arrow next to each device for more information about the connection. Wired Ethernet clients are not displayed
Click the Network tab at the top of the window to display more details about any Reserved IP address information or Port Mapping information that might have been set up on the AirPort router. If you have not configured any settings here, then the area will appear inactive.