Question

lg^2(x)+lg(2/x)+lg(5/x)=4

Answer 1

$log^{2} (x) + log( \frac{2}{x} ) + log( \frac{5}{x} ) = 4 \\ ОДЗ: x > 0 \\ log^{2} (x) + log(2) - log(x) + log(5) - log(x) = 4 \\ log^{2} (x) - 2 log(x) + log(2 \times 5) = 4 \\ log^{2} (x) - 2 log(x) + 1 - 4 = 0 \\ log^{2} (x) - 2 log(x) - 3 = 0 \\ Замена: log(x) = t \\ {t}^{2} - 2t - 3 = 0 \\ t_{1} = 3 \\ t_{2} = - 1 \\ Обратная \: замена: \\ log(x) = 3; \: x = {10}^{3} \\ log(x) = - 1; \: x = {10}^{ - 1}$

Ответ: 1000, 0.1