1)ОДЗ (x-√6)(x+√6)>0⇒x<-√6 U x>√6 U x≠0
x∈(-∞;-√6) U (√6;∞)
-log(3)(x²-6)+log(3)x≥0
log(3)[x/(x²-6)]≥0
x/(x²-6)≥1
(x²-x-6)/(x²-6)≤0
x²-x-6=0⇒x1+x2=1 U x1*x2=-6⇒x1=-2 U x2=3
+ _ + _ +
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-√6 -2 √6 3
x∈(√6;3]
2)ОДЗ 5-2x>0⇒x<2,5 U x>0 U x≠1
x∈(0;1) U (1;2,5)
log(3)√(5-2x)*1/log(3)x<1⇒log(x)√(5-2x)<1<br>a)x∈(0;1)
√(5-2x)>x
5-2x=x²
x²+2x-5<0<br>D=4+20=24
x1=(-2-2√6)/2=-1-√6 U -1+√6
-1-√6 x∈(0;1)
b)x∈(1;2,5)
x²+2x-5>0
x<-1-√6 U x>-1+√6
x∈(-1+√6;2,5)
Ответ x∈(0;1) U (-1+√6;2,5)
3)ОДЗ x>0 U x≠1
x∈(0;1)(1;∞)
2log(7)x -2/log(7)x<3<br>(2log(7)x-3log(7)x-2)/log(7)x<0⇒(log(7)x+2)/log(7)x>0
a)log(7)x+2>0⇒log(7)x>-2
log(7)x>0⇒x>1
2)a)log(7)x+2<0⇒log(7)x<-2⇒x<1/49<br>log(7)x<0<br>Ответ x∈(0;1/49) U (1/49;1)