1)2+3 normally is 5
to get 5 from 10, you multiply by 2

2)7+2 normally is 9
to get 63 from 9 you multiple by 7

*pattern recognition*

alter into mathematically neutral equations to check. Theoretically, if that is the pattern, every equation should fit.

1b) 2=x, 3=y. x+y=(x+y)*x!!!

Use other equation to check work (this is NOT guess and check. I did not arrive at the original answer by guessing)

2b) 7=y, 2=x. x+y=(x+y)*x!!

3b) 6+5=(6+5)*6 <---x+y=(x+y)*x (this is where I stopped)
4b) 8+4=+4)*8 <----x+y=(x+y)*x

Use projected solution to attempt to solve puzzle (again, this is not guess and check.)

9+7=(9+7)*9=144=correct


Strictly speaking, you are correct, it is not a "logical problem" (although I've seen PLENTY of published puzzles that are called logic problems that aren't.), but it is not merely "I'm going to randomly try shit until it works".

All that this problem required was the ability to break down the given "equations" and recognize the pattern when it danced in front of you like a naked marionette.

As mentioned, the "equation" presentation was a bit misleading, but I chose to present it how it was presented to me.