Before first: If your Mac is in default state, you probably do not see your system disk on you desktop. Go to
Finder>Preferences>General and tick the top two boxes (in fact, tick all four) so that your system disk and attached external disks are visible there.
First, make sure the sound library is fully installed on at least one of the system disks. Check the Sound Content Manager in Logic to verify everything is installed. Download whatever is reported as missing or incomplete, install it, then quit Logic.
What you need to do next is copy the Logic and Garageband folders that are inside the Library/Application support folder on your system disk to the external disk.
Third, after you've done that (make sure the copying is in fact finished, although Mac OS probably won't let you delete items that are still being copied), you can delete the original Application Support/Logic and -/Garageband folders from your sytem disk(s) (if they are on both).
Empty the trash.
Then, on the external, rightclick on the freshly copied Logic and Garageband folders and choose "create symbolic link" from the contextual menu. Note: do not relocate those folders on the external once you've created the symbolic links.
Then you need to copy those symbolic link files over to both system disks, inside the Library/Application Support folder. Finally, remove the word "symlink" from those filenames.
Now you should be good to go. Note that if you open Logic before you've attached the external disks, Logic will want to install a basic library, because it cannot see that the content is on an absent disk. So always make sure the external is plugged in before you open Logic.
That's how I've done it, and it works flawlessly.