Question

Найди корни уравнения: log0,1x(x)+log0,5x(x)=0.

Answer 1

x1 = 1

logx(x)/logx(0,1x) + logx(x)/logx(0,5x) = 0

logx(0,5x) + logx(0,1x) = 0

logx(0,5x) = logx(1/(0,1x))

0,5x = 1/0,1x

0,05x^2 = 1

x^2 = 20

x2 = 2sqrt{5}

Ответ: 1; 2sqrt{5}.