Take log\_2 on both sides to get (I'll simply write log here for simplicity)

>log 4\^x = log 3\^y

Using the fact that log (a\^b) = b log (a), we get

>x log4 = y log (3)

Since 2\^2 = 4 => log 4 = 2 and by division of y, it yields the desired result of

2x / y = log\_2 (3)