# If (√3)^5 x 9² = 3^n x 3√3, then value of n-

(a) n = 3

(b) n = 4

(c) n = 5

(d) None

**Answer: (c) n = 5**

**Solution:-**

(√3)^5 x 9^2 = 3^n x 3√3

(3)^5/2 x 3^4 = 3^n x 3^(1 + 1/2)

(3)^(5/2 + 4) = 3^3/2 x 3^n

(3)^13/2 = 3^n x 3^3/2

3^n = 3^(13/2 – 3/2)

3^n = 3^10/2

3^n = 3^5

Comparing on both side,

n = 5

Then, the value of n is 5.

Hence, the correct answer is option (c) n = 5.