I can't see a 'logout' button anywhere in the ux.stackexchange.com page. Advice was 'click on the 'StackExchange' logo (top left) to get the dropdown, but at present this just gets you a small screen of information about the Stack Exchange network.
Here is the logout link over here. you may be not observe some hidden things that is not so noticeable often. the logout link is not nested inside the stack-exchange logo. its inside a hamburger menu icon which is just look like Stack exchange logo . check bellow the difference between the logo and its menu icon.
if you are about to logout then you can use the link https://ux.stackexchange.com/users/logout
This is the way to logout of here.
The logo is actually on top right corner, next to question mark icon, achievements icon etc.