Question

решите логарифмическое уравнение

Answer 1

Ответ:

Замена:

$log_{5}(x) = t \\ x > 0 \: \: (odz)$

${t}^{2} = 3 t + 10 \\ {t}^{2} - 3 t - 10 = 0 \\ d = 9 + 40 = 49 \\ t1 = \frac{3 + 7}{2} = 5 \\ t2 = - 2 \\ \\ log_{5}(x) = 5 \\ x1 = {5}^{5} = 3125 \\ \\ log_{5}(x) = - 2 \\ x2 = {5}^{ - 2} = \frac{1}{25}$