1) Loq_0,5 (5x-2) < Loq_0,5 (3-2x) ;
5x-2> 3-2x >0 ;
5/7 < x < 3/2 . * * * x∈(5/7 ;1,5* * *<br>--------------------
2) Loq_3 (2x -7) < 0 ;<br>0 < 2x -7 <1 ;<br>7<2x <1+7 ;<br>7/2 -------------------
3) Loq_1/2 (x+3)/(x-1) > 1 ;
0 <(x+3)<strong>/(x-1) < 1/2 ;
a) (x+3)/(x-1) >0 ⇒ (1) x∈(-∞ ;-3) U (1 ;∞) .
------
б)(x+3)/(x-1) < 1/2 ;
(x+3)/(x-1) - 1/2 < 0 ;<br>(2x+6 -x+1)/2(x-1) <0 ;<br>(x+7)/(x-1) <0 ;<br>x∈( -7 ;1)
x∈ ( (-∞ ;-3) U (1 ;∞)) ⋂ (- 7 ;1 ) =(-7; -3) .