Solve for x in the equation: log₂ x + log₄ x = 6.

Answer and explanation

Correct answer: B. 16

  1. Step 1: Change base of log₄ x to base 2: log₄ x = (log₂ x) / (log₂ 4) = (log₂ x) / 2 = 0.5 log₂ x. Step 2. Substitute: log₂ x + 0.5 log₂ x = 6 => 1.5 log₂ x = 6. Step 3. Solve for log₂ x: log₂ x = 6 / 1.5 = 4. Step 4. Antilog: x = 2⁴ = 16. Answer: 16. Why not the others: 64 gives log₂ 64 + log₄ 64 = 6 + 3 = 9 ≠ 6; 8 gives 3 + 1.5 = 4.5 ≠ 6; 32 gives 5 + 2.5 = 7.5 ≠ 6.

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