Question

If log₆ (J) = log₂₄ (K) = x and G is geometric mean of J and K then find the value of log₁₂ (G) + (log₁₂ (G)) ² + 3x + 4, if x = 2

1. 14
2. 16
3. 15
4. 18

Answer 1

Correct Answer - Option 2 : 16

Calculation:

log₆ (J) = x

⇒ J = 6^x

⇒ log₂₄ K = x

⇒ K = 24^x

G = √(6^x × 24^x)

⇒ G = 12^x

log₁₂ (G) + (log₁₂ (G)) ² + 3x + 4

⇒ log12 (G) + 2(log12 (G)) + 3x + 4

⇒ x + 2x + 3x + 4

⇒ 2 + 4 + 6 + 4

∴ The required answer is 16

log₁₂ (G) = log₁₂ (12x)

⇒ log12 (12^x) = xlog12 (12)

⇒ log12 (G) = x

 Geometric mean for X₁, X₂, X₃.....X_n ⇒ g = (X₁ × X₂ × X₃ ....... X_n)^1/n