1
log(2)(2x-2)>log(2)(6-5x
{2x-2>0⇒2x>2⇒x>1
{6-5x>0⇒5x<6⇒x<1,2<br>{2x-2>6-5x⇒7x>8⇒x>1 1/7
x∈(1;1 1/7)
2
log(1/2)(5x-8)>1
{5x-8>0⇒5x>8⇒x>1,6
{5x-8<0,5⇒5x<8,5⇒x<1,7<br>x∈)1,6;1,7)
3
log(π)[(x-2)/(x-3)](x-2)/(x-3)>0
x=2 x=3
x<2 U x>3
(x-2)/(x-3)<3<br>(x-2)/(x-3)-3<0<br>(x-2-3x+9)/(x-3)<0<br>(7-2x)/(x-3)<0<br>x=3,5 x=3
x<3 U x>3,5
x∈(-∞;2) U (3,5;∞)
4
log(1/2)(2x-2)≥0
{2x-2>0⇒x>1
{2x-2≤1⇒x≤1,5
x∈(1;1,5]
5
log(4)x+log(4)(x-3)<1<br>{x>0
{x-3>0⇒x>3
{log(4)(x²-3x)<1⇒x²-3x<4⇒x²-3x-4<0⇒-1<x<4<br>x1+x2=3 U x1*x2=-4⇒x1=-1 U x2=4
x∈(3;4)