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micklson
@micklson
April 2021
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Решите Логарифмические неравенства
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sedinalana
Verified answer
2
ОДЗ
x-2>0⇒x>2
x>0
2x-3>0⇒x>1,5
x∈(2;∞)
log(0,2)[x(x-2)>log(0,2)(2x-3)
x²-2x<2x-3
x²-4x+3<0
x1+x2=4 U x1*x2=3
x1=1 u x2=3
1<x<3
x∈(2;3)
3
ОДЗ
36-x²≥0⇒-6≤x≤6
x>0
x∈(0;6]
√(36-x²)≥0⇒log(0,5)x/(x-2)≤0
1)log(0,5)x≥0⇒x≤1
x-2<0⇒x<2
0<x≤1
2)x≥1
x>2
2<x≤6
x∈(0;1] U (2;6]
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Answers & Comments
Verified answer
2ОДЗ
x-2>0⇒x>2
x>0
2x-3>0⇒x>1,5
x∈(2;∞)
log(0,2)[x(x-2)>log(0,2)(2x-3)
x²-2x<2x-3
x²-4x+3<0
x1+x2=4 U x1*x2=3
x1=1 u x2=3
1<x<3
x∈(2;3)
3
ОДЗ
36-x²≥0⇒-6≤x≤6
x>0
x∈(0;6]
√(36-x²)≥0⇒log(0,5)x/(x-2)≤0
1)log(0,5)x≥0⇒x≤1
x-2<0⇒x<2
0<x≤1
2)x≥1
x>2
2<x≤6
x∈(0;1] U (2;6]