If log₄ x = 2.5, the value of x is :

1. 12.5

2. 32

3. 10

4. 20

Given,

⇒ log₄ x = 2.5

⇒ x = 4^2.5

⇒ x = 4^{2 + 0.5}

⇒ x = 4².4^0.5

⇒ x = $16.(4)^{\dfrac{1}{2}}$

⇒ x = $16.(2^2)^{\dfrac{1}{2}}$

⇒ x = 16 × 2 = 32.

Hence, Option 2 is the correct option.