Single correct option
If log₂x + log₄x + log₁₆x = 21/4, then x equals
- A. 2√2
- B. 8
- C. 4
- D. 16
Show answer and solution
Answer: (B) 8
Convert all to base 2: log₄x = (log₂x)/2 and log₁₆x = (log₂x)/4.
So log₂x × (1 + 1/2 + 1/4) = 21/4 → log₂x × 7/4 = 21/4 → log₂x = 3 → x = 2³ = 8.
Check: log₂8 + log₄8 + log₁₆8 = 3 + 1.5 + 0.75 = 5.25 = 21/4 ✓.
So log₂x × (1 + 1/2 + 1/4) = 21/4 → log₂x × 7/4 = 21/4 → log₂x = 3 → x = 2³ = 8.
Check: log₂8 + log₄8 + log₁₆8 = 3 + 1.5 + 0.75 = 5.25 = 21/4 ✓.
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