Solve F(x,y)=0

I want to solve this problem

log((1+alpha1*x./(1+alpha2*y))) -lambda*log((1+beta1*x./(1+beta2*y)))-(x+y-P)==0

where

alpha1=1; alpha2=0.2; beta1=1; beta2=2; lambada=2; P=3;

Could you please give me some ways?

Many Thanks

[darova]

i'd use numerical approach - contour3