Single correct option
If log₃x + log₉x + log₂₇x = 22/3, then x equals
- A. 81
- B. 27
- C. 9
- D. 243
Show answer and solution
Answer: (A) 81
Convert everything to base 3: log₉x = (log₃x)/2 and log₂₇x = (log₃x)/3.
So log₃x (1 + 1/2 + 1/3) = (11/6) log₃x = 22/3, giving log₃x = (22/3) × (6/11) = 4.
Hence x = 3⁴ = 81.
Tip: log_{bⁿ} x = (1/n) log_b x — always change to the smallest common base.
So log₃x (1 + 1/2 + 1/3) = (11/6) log₃x = 22/3, giving log₃x = (22/3) × (6/11) = 4.
Hence x = 3⁴ = 81.
Tip: log_{bⁿ} x = (1/n) log_b x — always change to the smallest common base.
Saved on this device. Sign in or create a free account to keep it on every device.