Solve \(9^{2x + 1} = 81^{3x + 2}\)
FURTHER MATHEMATICS
WAEC 2011
Solve \(9^{2x + 1} = 81^{3x + 2}\)
- A. \(\frac{-3}{4}\)
- B. \(\frac{-2}{3}\)
- C. \(\frac{4}{5}\)
- D. \(\frac{3}{2}\)
Correct Answer: A. \(\frac{-3}{4}\)
Explanation
\(9^{2x + 1} = 81^{3x + 2}\)
\(9^{2x + 1} = (9^{2})^{3x + 2}\)
\(9^{2x + 1} = 9^{6x + 4}\)
Equating powers,
\(2x + 1 = 6x + 4 \implies -3 = 4x\)
\(\therefore x = \frac{-3}{4}\)
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