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

Given

`f(x,y) = 2ln(xy)=2ln(x)+2ln(y)`

to check whether the given function  is homogenous

then it has to be

`f(tx,ty)=t^n f(x,y)`

so ,

`f(tx,ty)=2ln(tx *ty) = 2ln(t^2 xy) = 2ln(t^2)+2ln(xy)`

`=4ln(t)+2ln(x)+2ln(y)`

which is not of the form` f(tx,ty)=t^n f(x,y)`

so the function is not Homogenous.