Single correct option
If log₃x + log₉x = 15/2, then x equals
- A. 81
- B. 3√3
- C. 243
- D. 27
Show answer and solution
Answer: (C) 243
Convert log₉x to base 3: log₉x = (log₃x)/2.
So log₃x (1 + 1/2) = (3/2)·log₃x = 15/2 ⇒ log₃x = 5 ⇒ x = 3⁵ = 243.
Check: log₃243 = 5, log₉243 = 2.5; sum = 7.5 = 15/2. ✓
Tip: log_{bⁿ}x = (1/n)·log_b x — use it to bring all logs to a common base.
So log₃x (1 + 1/2) = (3/2)·log₃x = 15/2 ⇒ log₃x = 5 ⇒ x = 3⁵ = 243.
Check: log₃243 = 5, log₉243 = 2.5; sum = 7.5 = 15/2. ✓
Tip: log_{bⁿ}x = (1/n)·log_b x — use it to bring all logs to a common base.
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