1
log(4)(x+6)+log(4)x=2
ОДЗ
{x+6>0⇒x>-6
{x>0
x∈(0;∞)
log(4)(x²+6x)=2
x²+6x=16
x²+6x-16=0
x1+x2=-6 U x1*x2=-16
x1=-8∉ОДЗ
x2=2
2
2log(5)x-log(x)5-1=0
ОДЗ
{x>0
{x≠1
x∈(0;1) U (1;∞)
2log(5)x-1/log(5)x -1=0
log(5)x=a
2a-1/a -1=0
2a²-a-1=0
D=1+8=9
a1=(1-3)/4=-2⇒log(5)x=-2⇒x=1/25
a2=(1+3)/4=1⇒log(5)x=1⇒x=5
3
log²(0,5)x-3log(0,5)x-4=0
x>0
log(0,5)x=a
a²-3a-4=0
a1+a2=3 U a1*a2=-4
a1=-1⇒log(0,5)x=-1⇒x=2
a2=4⇒log(0,5)x=4⇒x=1/16