Question

Помогите пожалуйста подробно решить неравенства. даю 28 баллов

Answer 1

71
ОДЗ
x²+8x-9>0
x1+x2=-8 U x1*x2=-9⇒x1=-9 U x2=1
x∈(-∞;-9) U (1;∞)
log(11)(x+9)³(x-1)³≤log(11)11^4(x-1)³/(x+9)
log(11)(x+9)³(x-1)³-log(11)11^4(x-1)³/(x+9)≤0
log(11)[(x+9)³(x-1)³*(x+9)/11^4(x-1)³]≤0
log(11)[(x+9)/11^4≤0
4log(11)(x+9)/11≤0
log(11)(x+9)/11≤0
(x+9)/11≤1
x+9≤11
x≤2
x∈(-∞;-9) U (1;2]
72
ОДЗ
x²+11x+30>0
x1+x2=-11 U x1*x2=30⇒x1=-6 U x2=-5
x∈(-∞;-6) U (-5;∞)
lg[(x+6)^11*(x+5)^11]≤lg[10^12(x+6)^11/(x+5)]
lg[(x+6)^11*(x+5)^11]-lg[10^12(x+6)^11/(x+5)]≤0
lg[(x+6)^11*(x+5)^11*(x+5)/10^12(x+6)^11]≤0
lg[(x+5)/10]^12≤0
12lg([(x+5)/10]≤0
lg([(x+5)/10]≤0
(x+5)/10≤1
x+5≤10
x≤5
x∈(-∞;-6)
73
ОДЗ
x+5>0⇒x>-5
x-1>0⇒x>1
x-1≠1⇒x≠2
x∈(1;2) U (2;∞)
log(3)(x+5)+3/3log(x-1)3≤3
log(3)(x+5)+1/log(x-1)3≤3
log(3)(x+5)+log(3)(x-1)≤3
log(3)(x+5)(x-1)≤3
(x+5)(x-1)≤27
x²-x+5x-5-27≤0
x²+4x-32≤0
x1+x2=-4 U x1*x2=-32⇒x1=-8 U x2=4
-8≤x≤4
x∈(1;2) U (2;4]