Deleting Logic is fairly straightfoward:
1. In the Finder, choose Applications from the Go menu.
2. Locate the Logic Pro X application and drag it to the trash.
3. Open the Mac App Store
4. Click the Purchases button in the Mac App Store toolbar.
5. Sign in to the Mac App Store using the Apple ID you first used to purchase Logic Pro X.
6. Look for Logic Pro X in the list of purchased applications in the App Store. If you don't see Logic Pro X in the list,make sure it's not hidden.
7. Click Install to download and install Logic Pro X.
Just to be safe, it might be a good idea to also delete all of your logic preferences:
1. In the Finder, choose Go to Folder from the Go menu.
2. Type ~/Library/Preferences in the "Go to the folder" field.
3. Press the Go button.
4. Remove all of the preferences that contain the word "logic" by dragging them to the trash.
5. Restart the computer.
This should do the trick.