PrepRung
Sign inSign up free

CAT 2020 Slot 2 · Quant · Logarithms and Indices · easy

If log₄x + log₁₆x + log₆₄x = 11, then x equals

Single correct option

If log₄x + log₁₆x + log₆₄x = 11, then x equals
  1. A. 1024
  2. B. 2048
  3. C. 4096
  4. D. 512
Show answer and solution

Answer: (C) 4096

Convert everything to base 4: log₁₆x = (log₄x)/2 and log₆₄x = (log₄x)/3 (since 16 = 4² and 64 = 4³).

So log₄x × (1 + 1/2 + 1/3) = 11 → (11/6) log₄x = 11 → log₄x = 6 → x = 4⁶ = 4096.

Check: log₄4096 + log₁₆4096 + log₆₄4096 = 6 + 3 + 2 = 11. ✓
Report a mistake

Original question written in the CAT 2020 Slot 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake