20
log²(5)x-2=3log(125)x
log²(5)x-2-log(125)x³=0
log(5³)x³=log(5)x
log²(5)x-log(5)x-2=0
log(5)x=a
a²-a-2=0
a1+a2=1 Ua1*a2=-2
a1=-1⇒log(5)x=-1⇒x=1/5
a2=2⇒log(5)x=2⇒x=25
21
log²(6)x+log(√6)x=log(0,5)2
log(√6)x=log(6)x/log(6)√6=log(6)x/(1/2)=2log(6)x
log(1/2)2=-1
log²(6)x+2log(6)x+1=0
(log(6)x+1)²=0
log(6)x+1=0
log(6)x=-1
x=1/6
22
log(2)x-2log(x)2=-1
ОДЗ: x>0 U x≠1
log(2)x-2log(2)2/log(2)x+1=0
log(2)x-2/log(2)x+1=0
log²(2)x+log(2)x-2=0
log(2)x=a
a²+a-2=0
a1+a2=-1 U a1*a2=-2
a1=-2⇒log(2)x=-2⇒x=1/4
a2=1⇒log(2)x=1⇒x=2