First, you are going to need v9.1.7 or later with Mountain Lion (http://support.apple.com/kb/HT5421)
To get the updaters to work several things MUST be correct:
The Logic Application must be named "Logic Pro" or "Logic Express" (depending on which type you are working with) with NO Additional spaces or numbers in the name.
The application must be at the root level of the Applications folder (and NOT anywhere else).
i have the same problem joefish132 has,
i brought logic express 9 in 2010. then havnt used it for a couple of years. i have upgraded my mac to osx 10.8.5 and havnt upgraded any of logic. now im trying to open it and it says what joefish has explained above. ive also tried renaming and upgrading but still nothing. can you help me out please. cheers