Question

Решите уравнение 

lg^2 x + 4 lg x/10=1

Answer 1

 

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