JAMB 2012 Mathematics · Question 9
If log3x2 = -8, what is x?
Options
- A.
- B.
- C.
- D.
Answer: D.
Explanation written with AI and checked against the answer key
Analyze the question: The notation "log3x2 = -8" is ambiguous. The standard JAMB version reads log₃ x² = -8, though it could also be read as log₃(x)² or (log₃ x)². I'll go with log base 3 of x², which is the intended reading. Concept: log_b N = p means N = b^p. Solution: log₃ x² = -8 x² = 3⁻⁸ x² = 1/3⁸ Take the square root of both sides: x = ±1/3⁴ = ±1/81 Since a logarithm needs a positive argument, x² is positive for either sign. But x = -1/81 is also valid here, because x² > 0. The positive value, 1/81, is the one that matches the options. Alternatively, using the power rule: 2 log₃ x = -8, so log₃ x = -4, and x = 3⁻⁴ = 1/81. This gives the same value. Check: (1/81)² = 1/6561 = 3⁻⁸, and log₃(3⁻⁸) = -8. ✓ Answer: D (1/81) Tip: When the log has a power inside, either convert directly to index form, or bring the power down first (log x² = 2 log x). Then remember that a negative index means a reciprocal: 3⁻⁴ = 1/3⁴. Always check by substituting back.AI can make mistakes. Report anything that looks wrong.
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