`f(x,y) = 2ln(x/y)` Determine whether the function is homogenous and if it is, determine its degree

A function `f(x, y)` is called homogenous (homogeneous) of degree `n,` if for any `x,` `y` we have `f(tx, ty) = t^n f(x, y).`

The given function is homogenous of degree 0, because

`f(tx, ty) = 2ln((tx)/(ty)) = 2ln(x/y) = f(x, y) = t^0 f(x,y).`

The difficulty is that this function is not defined for all `x` and `y.` The above equality is true for all `x` and `y` for which it has sense.