Question

Решите уравнение $lg(0,1x^2)*lgx=1$.

Answer 1

{x > 0}
lg(x^2/10) * lgx = 1
(lg(x^2) - lg(10)) * lgx = 1
(2lgx - 1) * lgx = 1
{lgx = t}
2t^2 - t - 1 = 0
(2t + 1)(t - 1) = 0
t = 1 -> lgx = 1 -> x = 10
t = -1/2 -> lgx = -1/2 -> x = 1/sqrt(10)

{действительно, при
x = 10, lg(1/10 * 100) * lg10 = lg10 * lg10 = 1*1 = 1
x = 1/sqrt(10), lg(1/10 * 1/10) * lg(1/sqrt(10)) = (-2) * (-1/2) = 1 }