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