Xueqin!

This happened in "backyard monsters". I am Xueqin.

TheFacelessOne: ><
Cefia: Lol, it is always you who kills the chat. <3
TheFacelessOne: It is. >< I don't like it...
Xueqin: OMFG IT'S THE FAMOUS THEFACELESSONE
TheFacelessOne: Hello there.
Cefia: O.o
Cefia: And nothing.
TheFacelessOne: Of course not, I mean... I had the last message.
Gaggelini: Was it irony or true adoration, we will never know ...

I have edited a version of Pr3 so you can make levels with 270:00+ time. Should I make a thread for it or not? (I will give the link. )

Can someone please help me solve this? Thanks in advance!

log9(X)=log12(Y)=log16(X+Y) and both X and Y are positive.

Find X/Y.

Answer: (√5 -1)/2