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

a/2

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 Correct Answer a

Calculation:

⇒ log₃ x = log₁₂y = a,

⇒ log₃ x = a, x = 3^a

⇒ log₁₂y = 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.

Feb 20, 2025

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