If you've entered the path manually you don't need to hit the 'Obtain' button. You can test to see if you have the correct path by jumping to another system and seeing if EDDI tells you about your destination.
As it says in the text on the screen, you can use the 'Obtain' button to obtain the log path as long as you have Elite running and you are running EDDI from a local administrator account.
Nothing, doesn't work. I'm using the local administrator account, tried clicking obtain, then also tried writing down the path manually without hitting obtain, eddi doesn't think it's the right folder and I don't know why.