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CAT 2021 Slot 2 · Quant · Logarithms and Indices · easy

If log₃x + log₉x + log₂₇x = 11/3, then x equals

Single correct option

If log₃x + log₉x + log₂₇x = 11/3, then x equals
  1. A. 3
  2. B. 6
  3. C. 9
  4. D. 27
Show answer and solution

Answer: (C) 9

Convert everything to base 3: log₉x = (log₃x)/2 and log₂₇x = (log₃x)/3.

So log₃x × (1 + 1/2 + 1/3) = 11/3 ⇒ (11/6) log₃x = 11/3 ⇒ log₃x = 2 ⇒ x = 9.

Check: log₃9 + log₉9 + log₂₇9 = 2 + 1 + 2/3 = 11/3 ✓.
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Original question written in the CAT 2021 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