Express the following in a form free from logarithm :

a log x - b log y = 2 log 3

Given,

⇒ a log x - b log y = 2 log 3

⇒ log x^a - log y^b = log 3²

⇒ log $\Big(\dfrac{x^a}{y^b}\Big)$ = log 3²

⇒ log $\Big(\dfrac{x^a}{y^b}\Big)$ = log 9

⇒ $\Big(\dfrac{x^a}{y^b}\Big) = 9$

⇒ x^a = 9y^b.

Hence, required equation is x^a = 9y^b.