Solve \(9^{2x + 1} = 81^{3x + 2}\)

  • A \(\frac{-3}{4}\)
  • B \(\frac{-2}{3}\)
  • C \(\frac{4}{5}\)
  • D \(\frac{3}{2}\)
waec 2011furthermathematics

The correct answer is A. \(\frac{-3}{4}\)

\(9^{2x + 1} = 81^{3x + 2}\)

\(9^{2x + 1} = (9^{2})^{3x + 2}\)

\(9^{2x + 1} = 9^{6x + 4}\)

Equating powers, 

\(2x + 1 = 6x + 4 \implies -3 = 4x\)

\(\therefore x = \frac{-3}{4}\)

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