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kobzarenko99
@kobzarenko99
September 2021
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Плиз срочно 7,8,9 даю 20 Балов
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oganesbagoyan
Verified answer
7)
Loq_1/3 (x+3) > -1 ;
т.к 0<1/3<1 то :
0< x+3 < (1/3) ^(-1) ;
0< x+3 < 3;
-3 < x < 0 ;
⇔x∈(-3 ;0) →
Б
------------------
8)
xLoq_1/2 5 < Loq_1/2 3;
т.к 0<1/2<1 ; то (Loq_1/2 5) <0 :
x > Loq_1/2 3/Loq_1/2 5 ;
x> Loq_5 3
.⇔(Loq_5 3 ;∞)
→В
9)
Loq_x (4x+5)/(6-5x) = -1 .
ОДЗ:{ x>0 ;x ≠ 1; 4x+5)/(6-5x >0 .
(4x+5)/(6-5x) =1/x ;
4x² +5x = 6 -5x ;
4x² +10x -6 = 0;
2x² +5x -3 =0;
D =5² -4*2(-3) = 49 =7² ;
x₁ = (-5-7)/4 = -3 ∉ ОДЗ .
x₂ =(-5+7)/4 =1/2.
ответ : 1/2.
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Answers & Comments
Verified answer
7) Loq_1/3 (x+3) > -1 ;т.к 0<1/3<1 то :
0< x+3 < (1/3) ^(-1) ;
0< x+3 < 3;
-3 < x < 0 ;
⇔x∈(-3 ;0) →Б
------------------
8) xLoq_1/2 5 < Loq_1/2 3;
т.к 0<1/2<1 ; то (Loq_1/2 5) <0 :
x > Loq_1/2 3/Loq_1/2 5 ;
x> Loq_5 3
.⇔(Loq_5 3 ;∞) →В
9) Loq_x (4x+5)/(6-5x) = -1 .
ОДЗ:{ x>0 ;x ≠ 1; 4x+5)/(6-5x >0 .
(4x+5)/(6-5x) =1/x ;
4x² +5x = 6 -5x ;
4x² +10x -6 = 0;
2x² +5x -3 =0;
D =5² -4*2(-3) = 49 =7² ;
x₁ = (-5-7)/4 = -3 ∉ ОДЗ .
x₂ =(-5+7)/4 =1/2.
ответ : 1/2.