Question

Suppose, log₃ x = log₁₂ y = a, where x, y are positive numbers. If G is the geometric mean of x and y, and log₆ G is equal to
1. \(\sqrt{a}\)
2. 2a
3. a/2
4. a

Answer 1

Correct Answer - Option 4 : a

Calculation:

⇒ log₃ x = log₁₂ y = a,

⇒ log₃ x = a, x = 3^a

⇒ log₁₂ y = a, y = 12^a

⇒ If G is geometric mean = √xy = √(36^a)

⇒ √(6^2a) = (6^2a)^1/2

⇒ 6^a

⇒ log₆ G = a

∴ The required result will be a.