Single correct option
If log₅x + log₂₅x + log₁₂₅x = 11/2, then x equals
- A. 125
- B. 25
- C. 5
- D. 625
Show answer and solution
Answer: (A) 125
Convert everything to base 5: log₂₅x = (log₅x)/2 and log₁₂₅x = (log₅x)/3.
So log₅x × (1 + 1/2 + 1/3) = (11/6) log₅x = 11/2, which gives log₅x = 3 and x = 125.
Check: log₅125 = 3, log₂₅125 = 1.5, log₁₂₅125 = 1; sum = 5.5 = 11/2. ✓
Tip: log_{bⁿ}x = (1/n) log_b x.
So log₅x × (1 + 1/2 + 1/3) = (11/6) log₅x = 11/2, which gives log₅x = 3 and x = 125.
Check: log₅125 = 3, log₂₅125 = 1.5, log₁₂₅125 = 1; sum = 5.5 = 11/2. ✓
Tip: log_{bⁿ}x = (1/n) log_b x.
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