Given: (√3)5×92=3n×3√3 Concept Used: By using the law of indices∶ am×an=a(m+n) am÷an=a(m–n) [(am)n]=amn (a)(−m)=
1
am
(a)(
m
n
)=n√am (a)0 = 1 Calculation: The equation will be solved as: (√3)5×92=3n×3√3 (√3)4×√3×92=3n×3√3 ⇒ 9√3×92=3n×3√3 ⇒ 3√3×35=3n×3√3 ⇒ 35=3n ⇒ n = 5 ∴ Value of n is 5