Solution of given equations for $x$ and $y$

Question

Solve for $x$ and $y$

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

$$3^{\log x}=2^{\log y}$$

Could someone give some hint to approach this question?

Answer 1

Let $\log x = s$, $\log y = t$, and take logs of both sides of the equations. You get a system of two linear equations in $s$ and $t$.