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Nadia1999
@Nadia1999
August 2022
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sedinalana
Verified answer
1
ОДЗ
2x-1>0⇒x>1/2
2x-1=9
2x=10
x=5
Ответ x=5
2
ОДЗ
{3-x>0⇒x<3
{x+2>0⇒x>-2
x∈(-2;3)
lg[(3-x)/(x+2)]=lg4
(3-x)/(x+2)=4
3-x=4x+8
4x+x=3-8
5x=-58
x=-1
Ответ x=-1
3
ОДЗ
{x+1>0⇒x>-1
{4x-5>0⇒x>1,25
x∈(1,25;∞)
x+1=4x-5
4x-x=1+5
3x=6
x=2
Ответ x=2
4
ОДЗ x>0
log(5)x=a
2a²-7a+3=0
D=49-24=25
a1=(7-5)/4=0,5⇒log(5)x=0,5⇒x=√5
a2=(7+5)/4=3⇒log(5)x=3⇒x=125
5
log(3)x=a
2a²-2a-4=0
a²-a-2=0
a1+a2=1 U a1*a2=-2
a1=-1⇒log(3)x=-1⇒x=1/3
a2=2⇒log(3)x=2⇒x=9
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Answers & Comments
Verified answer
1ОДЗ
2x-1>0⇒x>1/2
2x-1=9
2x=10
x=5
Ответ x=5
2
ОДЗ
{3-x>0⇒x<3
{x+2>0⇒x>-2
x∈(-2;3)
lg[(3-x)/(x+2)]=lg4
(3-x)/(x+2)=4
3-x=4x+8
4x+x=3-8
5x=-58
x=-1
Ответ x=-1
3
ОДЗ
{x+1>0⇒x>-1
{4x-5>0⇒x>1,25
x∈(1,25;∞)
x+1=4x-5
4x-x=1+5
3x=6
x=2
Ответ x=2
4
ОДЗ x>0
log(5)x=a
2a²-7a+3=0
D=49-24=25
a1=(7-5)/4=0,5⇒log(5)x=0,5⇒x=√5
a2=(7+5)/4=3⇒log(5)x=3⇒x=125
5
log(3)x=a
2a²-2a-4=0
a²-a-2=0
a1+a2=1 U a1*a2=-2
a1=-1⇒log(3)x=-1⇒x=1/3
a2=2⇒log(3)x=2⇒x=9