Correct Answer - Option 4 : 2

**Calculation:**

5(x + 1) + 5(2 - x) = 53 + 1

⇒ 5^{x} × 5 + 5^{2} × 5^{-x} = 125 + 1 = 126

⇒ 5y + 25/y = 126 ----(1) where, y = 5^{x}

⇒ 5y^{2} - 126y + 25 = 0

⇒ 5y^{2} - 125y - y + 25 = 0

⇒ 5y(y - 5) - (y - 25) = 0

⇒ (5y - 1)(y - 25) = 0

⇒ y = 1/5 or y = 25

When, y = 1

⇒ 5^{x} = 1/5 = 5^{-1}

⇒ x = -1, which is not possible as we need only +ve value of x.

And, when y = 25

⇒ 5^{x} = 25 = 5^{2}

x = 2 which is +ve

**∴ The positive value of x is 2.**