Solving the system $\ln(xy)=4$ and $(\ln x)(\ln y)=-12$

Question

If we have this system: $$\begin{align} \ln(xy) &=\phantom{-1}4 \\ (\ln x)(\ln y) &=-12 \end{align}$$

I know that $\ln(xy)= \ln x + \ln y$ to solve for $x$ and $y$, but what is $(\ln x)(\ln y)$?

How can I solve this ?

Answer 1

Hint: $$\ln(xy)=\ln(x)+\ln(y)$$ Let $$a=\ln(x),b=\ln(y)$$ then you will get $$a=\ln(x),b=\ln(y)$$ then we get $$a+b=4$$ and $$ab=-12$$