# How to compute Walrasian equilibrium in the case of logarithmic utility?

If the utility is $$U = \ln x + 2 \ln y$$, how do you compute Walrasian equilibrium via usual formula for demand $$x=a(x p_x + y p_y)/p_x(a+b)$$ ?

What is $$a$$ and $$b$$?

In case of Cobb-Douglas function like $$U=x^3y^4$$ it would be simple: $$a=3$$ and $$b=4$$, but in this case how is it computed?

let $$u \equiv xy^2$$, then we have: $$U=lnx+2lny=ln(xy^2)=ln(u)$$ Since $$U'(u)>0 \: \forall u>0$$ it follows that the $$(x,y)$$ that maximizes $$U$$ also maximizes $$u$$; $$\max \{U\}=\max\{ln(u)\}=ln(\max\{u\})$$. $$u$$ represents the same preferences as $$U$$.
Clearly, $$u(x,y)=x^a y^b$$ with $$a=1$$, $$b=2$$.