Question

ДАМ 20 БАЛЛОВ. ЛОГАРИФМЫ. ПОМОГИТЕ ПОЖАЛУЙСТА​

Answer 1

Ответ:

$log_{2} {}^{2} ( {x}^{2} ) - 16 log_{2}(2x) + 31 = 0 \\ {2}^{2} log_{2} {}^{2} (x) - 16 log_{2}(2) - 16 log_{2}(x) + 31 = 0 \\ 4 log_{2} {}^{2} (x) - 16 - 16log_{2}(x) + 31 = 0 \\ 4log_{2} {}^{2} (x) - 16 log_{2}(x) + 15 = 0 \\ \\ log_{2}(x) = t \\ \\ 4t {}^{2} - 16 t + 15 = 0\\ D = 256 - 240 = 16\\ t_1 = \frac{16 + 4}{8} = \frac{5}{2} = 2.5 \\ t_2 = \frac{3}{2} = 1.5 \\ \\ log_{2}(x) = 2.5 \\ x_1= {2}^{2.5} \\ x_1 = 4 \sqrt{2} \\ \\ log_{2}(x) = 1.5 \\ x_2 = {2}^{1.5} \\ x_2 = 2 \sqrt{2}$

Ответ:

$2 \sqrt{2} ;4 \sqrt{2}$