1)log0.25(x^2-3x)=-1 2) Log0.5(3x+0,5)+log0.5(x-2)=-2

Question

1)log0.25(x^2-3x)=-1
2) Log0.5(3x+0,5)+log0.5(x-2)=-2

Answer 1

1
x²-3x>0
x(x-3)>0
x=0  x=3
x∈(-∞;0) U (3;∞)
x²-3x=4
x²-3x-4=0
x1+x2=3 U x1*x2=-4
x1=-1 U x2=4
2
{3x+0,5>0⇒3x>-1/2⇒x>-1/6
{x-2>0⇒x>2
x∈(2;∞)
log(0,5)[(3x+0,5)(x-2)]=-2
3x²-6x+0,5x-1=4
3x²-5,5x-5=0
D=30,25+60=90,25
√D=9,5
x1=(5,5-9,5)/6=-2/3 не удов усл
x2=(5,5+9,5)/6=2,5