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Logic is a pro-app so it actually installs other stuff in other places.
Removing the main logic app will leave a fair amount of stuff still on the machine including the apple loops which will account for most of the disc space logic takes up.
This document here details what you need to remove if you want everything to go.
In most cases just dragging the icon to the trash folder will remove it, but logic is one of the pro-apps, so it installs stuff that other pro-apps can use.
No worries. Logic is a bit of a strange one because of all the content it installs and makes available to all other pro-apps.
Nearly every other mac app can be uninstalled in the copy to trash manner.
Most apps (that is, if they created a plist) will leave behind their preferences in the ~/Library folder.
Something like AppZapper should remove all stuff, but the data stored in the ~/Library folder will be minute and will not affect the performance of OS X, so it's nothing to worry about.