Question

Решите уравнение lg^2 x + 4 lg x/10=1

Answer 1

 

$lg^2 x + 4 lg x/10=1\\\\ lg^2 x + 4 lg x + 4 lg 10^{-1}=1\\\\ lg^2 x + 4 lg x - 4 lg 10 = 1\\\\ lg^2 x + 4 lg x - 4 = 1\\\\ lgx = t\\\\ x > 0\\\\ t^2 + 4t - 5 = 0\\\\ t_1*t_2 = -5\\\\ t_1 + t_2 = -4\\\\ t_1 = 1, t_2 = -5\\\\ lgx = 1, x = 10\\\\ lgx = -5, x = 1/100000$