Question

Решите уравнение
a) $27^{3x} =\frac{1}{3}$
б)$5^{2x+1} -5^{x}=4$

Answer 1

$a) {3}^{9x} = {3}^{ - 1} \\ 9x = - 1 \\ x = - \frac{1}{9}$
${5}^{2x} \times 5 - {5}^{x} - 4 = 0 \\ {5}^{x} = a \\ 5 {a}^{2} - a - 4 = 0 \\ d = 1 - 4 \times 5 \times ( - 4) = 81 \\ a1 = \frac{ - ( - 1) - \sqrt{81} }{2 \times 5} = \frac{1 - 9}{10} = - 0.8 \\ a2 = \frac{ - ( - 1) + 9}{2 \times 5} = \frac{10}{10} = 1 \\ {5}^{x} = - 0.8 \: ne \: mozhet \: byt \\ {5}^{x} = 1 \\ x = 0$