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nika2604201
@nika2604201
July 2022
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sangers1959
Verified answer
1.
log₂x>3 ОДЗ: x>0
x>2³
x>8
2.
log₁/₃(2x)>-2 ОДЗ: 2x>0 x>0
2x<(1/3)⁻²
2x<3²
x∈(0;4,5).
3.
log₅(3x-1)<1 ОДЗ: 3x-1>0 x>1/3
3x-1<1⁵
3x<2
x<2/3 ⇒
x∈(1/3;2/3).
4.
log₃(2-4x)≤1 ОДЗ: 2-4x>0 x<1/2
2-4x≤3¹
4x≥-1
x≥-1/4 ⇒
x∈[-1/4;1/2).
5.
log₀,₅(1+2x)>-1 ОДЗ: 1+2x>0 x>-1/2
1+2x<(1/2)⁻¹
1+2x<2
x<1/2 ⇒
x∈(-1/2;1/2).
6.
log₁/₇(5x+3)≥-1/2 ОДЗ: 5x+3>0 x>-0,6
5x+3≤(1/7)⁻¹/²
5x+3≤√7
5x≤√7-3
x≤(√7-3)/5 ⇒
x∈(-0,6;(√7-3)/5).
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Answers & Comments
Verified answer
1.log₂x>3 ОДЗ: x>0
x>2³
x>8
2.
log₁/₃(2x)>-2 ОДЗ: 2x>0 x>0
2x<(1/3)⁻²
2x<3²
x∈(0;4,5).
3.
log₅(3x-1)<1 ОДЗ: 3x-1>0 x>1/3
3x-1<1⁵
3x<2
x<2/3 ⇒
x∈(1/3;2/3).
4.
log₃(2-4x)≤1 ОДЗ: 2-4x>0 x<1/2
2-4x≤3¹
4x≥-1
x≥-1/4 ⇒
x∈[-1/4;1/2).
5.
log₀,₅(1+2x)>-1 ОДЗ: 1+2x>0 x>-1/2
1+2x<(1/2)⁻¹
1+2x<2
x<1/2 ⇒
x∈(-1/2;1/2).
6.
log₁/₇(5x+3)≥-1/2 ОДЗ: 5x+3>0 x>-0,6
5x+3≤(1/7)⁻¹/²
5x+3≤√7
5x≤√7-3
x≤(√7-3)/5 ⇒
x∈(-0,6;(√7-3)/5).