(log0,5 x)*(1+log0,5 8/x)+3=0

Question

(log0,5 x)*(1+log0,5 8/x)+3=0

Answer 1

(log0,5 x)*(1+log0,5 8/x)+3=0                  ОДЗ  x>0
(log0,5 x)*(1+log0,5 8-log0,5x)+3=0
(log0,5 x)*(1-3-log0,5 x)+3=0
(log0,5 x)*(-2-log0,5 x)+3=0
(log0,5 x)²+2(log0,5 x)-3=0
(log0,5 x)=a
a²+2a-3=0
a1+a2=-2 U a1*a2=-3
a1=-3⇒(log0,5 x)=-3⇒x=8
a2=1⇒(log0,5 x)=1⇒x=0,5