Logarithm question-I donot know but this question may be solved by any other way also.

Let $({x}_{0},{y}_{0})$ be the solution of the following equations.

$(2x{)}^{\mathrm{ln}2}=(3y{)}^{\mathrm{ln}3}$

${3}^{\mathrm{ln}x}={2}^{\mathrm{ln}y}$

Then ${x}_{0}$ is

A) $\frac{1}{6}$

B) $\frac{1}{3}$

C) $\frac{1}{2}$

D) $6$

I have tried this problem by taking log on both sides of the two equations. But, finally I could not make up to get the values of $x$ and $y$

Let $({x}_{0},{y}_{0})$ be the solution of the following equations.

$(2x{)}^{\mathrm{ln}2}=(3y{)}^{\mathrm{ln}3}$

${3}^{\mathrm{ln}x}={2}^{\mathrm{ln}y}$

Then ${x}_{0}$ is

A) $\frac{1}{6}$

B) $\frac{1}{3}$

C) $\frac{1}{2}$

D) $6$

I have tried this problem by taking log on both sides of the two equations. But, finally I could not make up to get the values of $x$ and $y$