Solving for $Y$, using a utility function

Question

The question asks to solve for $Y$, below are the steps I tried to use:

$U = \ln X + 3 \ln Y \iff U = \ln X + \ln Y^3 \iff \ln Y^3 = U - \ln X$

How can I move on from here if I need to isolate, why?

Answer 1

You can express it using the exponential function \begin{eqnarray} U= \ln{X} + 3\ln{y}\\ \ln{y}=\frac{U-\ln{X}}{3}\\ y=X^{-\frac{1}{3}}\exp{\frac{U}{3}} \end{eqnarray}