Multivariable limit $\lim_{(x,y)\to(0,0)}\frac{\ln(\cos(x^2+y^2))}{\ln(\cos(3x^2+3y^2))}$

I came today across the following problem:$$\lim_{(x,y)\to(0,0)}\frac{\ln(\cos(x^2+y^2))}{\ln(\cos(3x^2+3y^2))}$$My first thought was to substitute $$x^2 + y^2 = t$$ and solve the limit using l'Hopital.I am not really sure whether this method is correct. Both expressions in nominator and denominator are not differentiable in some intervals. I would like to know whether this doesn't interfere with the usage of l'Hopital rule in this example.