Question

Помогите решить уравнение

Answer 1

$lg ^{2} x + lg \: x ^{2} = lg ^{2} 2 - 1 \\ lg ^{2} x +2 lg \: x + 1 = lg ^{2} 2 \\ (lgx + 1) ^{2} = lg ^{2} 2 \\ {lg}^{2} (10x) - lg ^{2} 2 = 0 \\ ({lg} (10x) - lg 2)({lg} (10x) + lg 2) = 0 \\ lg10x = lg2 \\ x1 = \frac{1}{5} \\ 10x = \frac{1}{2} \\ x2 = \frac{1}{20}$