What value of n makes the equation true (2x^9y^y) (4x^2 y^10) = 8x^11y^20

Given that:

(2x^9y^n) (4x^2y^10) = 8x^11y^20

the value of n that will make the inequality true will be fond as follows;

(2x^9y^n) (4x^2y^10) = 8x^11y^ (n+10)

thus;

8x^11y^ (n+10) = 8x^11y^20

dividing through by 8x^11 we get;

y^ (n+10) = y^20

introducing the natural logs we get;

(n+10) lny=20lny

lny will cancel out and we shall remain with;

n+10=20

thus

n=20-10

n=10

the answer is n=10