Answer:
[tex] x = - \frac{1}{4} [/tex]
Step-by-step explanation:
[tex]{9}^{2x + 1} = {81}^{3x + 1} \\ \\{3}^{2(2x + 1)} = {3}^{4(3x + 1)} \\ \\ {3}^{4x + 2} = {3}^{12x + 4} \\ bases \: are \: equal \: so \: exponents \: \\ will \: also \: be \: equal\\ \\ 4x + 2 = 12x + 4 \\ \\ 2 - 4 = 12x - 4x \\ \\ - 2 = 8x \\ \\ x = - \frac{2}{8}\\ \\ x = - \frac{1}{4} [/tex]
