## Empty one year ago Solve: f(x,y)*f(y,x)=f(x,y)+f(y,x)

1. Empty

I promise to share the solutions I've found if you try. And my answers aren't trivial, they're dependent on x and y.

2. anonymous

:D

3. Empty

So here's the answer I found: $f(x,y)=1+\log_xy$ I honestly have no clue how I would find this sort of thing naturally, it came up when I was considering some interesting properties of logarithms, such as: $\log_a b \log_b a = 1$ $\log_a b \log_b c \log_ca= 1$ Specifically I've just been looking for something so that $f(a,b) * \log_a b = \delta_{ab}$ since this could be used to factor any number possibly easily with linear algebra.