Question

Решите пожалуйста уравнение

Answer 1

$log_{0.5}^{2}(x) - log_{0.5}(x) - 2 = 0 \\ t = log_{0.5}(x) \\ t^{2} - t - 2 = 0 \ \textless \ =\ \textgreater \ \\ t = 2 || t = -1 \ \textless \ =\ \textgreater \ \\ log_{0.5}(x) = 2 || log_{0.5}(x) = -1 \ \textless \ =\ \textgreater \ \\ x = 0.25 || x = 2$
'||' - это, типа, 'или'...
Если не отображается:
(log0.5(x))^2 - log0.5(x) - 2 = 0
t = log0.5(x)
t^2 - t - 2 = 0
<=> t = 2 || t = -1
log0.5(x) = 2 || log0.5(x) = -1
<=> x = 0.25 || x = 2