Question

Como resolve essa equação exponencial

9 ͯ - 4 . 3 ͯ + 3 = 0

Answer 1

$\red{x _{1} = 0 \: \: \: x_{2} = 1}$

explicação passo a passo

$\blue{9 {}^{x} - 4 \times 3 {}^{x} + 3 = 0 } \\ 9 {}^{x} - 4 \times 3 {}^{x} + 3 = 0 \\ (3 {}^{2}) {}^{x} - 4 \times 3 {}^{x} + 3 = 0 \\ (3 {}^{x}) {}^{2} - 4 \times 3 {}^{x} + 3 = 0 \\ t {}^{2} - 4t + 3 = 0 \\ t {}^{2} - t - 3t + 3 = 0 \\ t \times (t - 1) - 3t + 3 = 0 \\ t {}^{2} - t - 3t + 3 = 0 \\ t \times (t - 1) - 3(t - 1) = 0 \\ (t - 1) \times ( - 3) = 0 \\ t -1 = 0 \\ t -3 = 0 \\ t = 1 \\ t - 3 = 0 \\ t - 1 = 0 \\ t - 3 = 0 \\ t = 1 \\ t = 3 \\ t {}^{2} - 4t + 3 = 0 \\ t = 1 \\ t = 3 \\ 3 {}^{x} = 1 \\ 3 {}^{x} = 3 \\ 3 {}^{x} = 1 \\ 3 {}^{x} = 3 \\ x = 0 \\ 3 {}^{x} = 1 \\ 3 {}^{x} = 3 \\ x = 0 \\ 3 {}^{x} = 3 \\ 3 {}^{x} = 3 {}^{1} \\ x = 1 \\ 3 {}^{x} = 1 \\ 3 {}^{x} = 3 \\ x = 0 \\ x = 1 \\ x _{1} = 0 \: \: \: x_{2} = 1 \\ resposta \\ x_{1} = 0 \: \: \: x_{2} = 1$