I lost my Logic 9 serial, i had moved house and we were flooded out about 6 months before i lost it and had to chuck a lot of paperwork out that was caught in the water. I wanted to put it on to my new mac, and like a fool i had uninstalled it from my older iMac so was left with nothing but the disks.
Contacted Apple and they were no help whatsoever for me, i was really annoyed with them, complained and hit a brick wall where they couldn't offer to help as i could find no receipt either, never offered to check their system for me.
Luckily i had put the serial number in my old iMac box, which i didn't discover until a few weeks later, along with the receipt.
I was so pleased to find it! 🙂 ...but i do resent Apple a little after my dealings, really felt hung out to dry. As LP9 had just appeared on the app store at the time i did wonder if they were trying to drop any 'old school' boxed LP9/Logic Studio enquiries.
If they do provide you with a new serial, i beleive there's a fee for it too from my correspondance so it may be worth checking out what that is first, and whether you're best putting that into Logic Pro X.
Also, if you have Logic running on any of your old machines i think you can go to the About menu and it's displayed on there.
