Solve \(9^{2x + 1} = 81^{3x + 2}\)
\(9^{2x + 1} = 81^{3x + 2}\)
\(9^{2x + 1} = (9^{2})^{3x + 2}\)
\(9^{2x + 1} = 9^{6x + 4}\)
Equating powers,
\(2x + 1 = 6x + 4 \implies -3 = 4x\)
\(\therefore x = \frac{-3}{4}\)
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