After update Logic Pro X 10.5.1 won't boot up. 'Can't get core function pointer' dialogue box continuously pops up. Help!

You’ve just updated logic I’m presuming? From what version?

the move to 10.5.1will force logic to rescan all third party AUs You have and there are reported issues of problems with some Waves, NI and Izotope plugins. Some of this is being addressed by the developers, but it may be worth checking your plugins.

if all that is ok, it may be worth reinstalling logic.

That is an Audio Unit having issues. You probably need to find out, which Audio Unit complains.