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lenaskipina
@lenaskipina
June 2022
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Помогите решить )
Решить уравнение log4( 2x+3)=2
Решить неравенство log5(x-4)>-1
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m11m
Verified answer
1)
log₄ (2x+3)=2
ОДЗ: 2x+3>0
2x> -3
x> -1.5
2x+3=4²
2x+3=16
2x=16-3
2x=13
x=6.5
Ответ: 6,5
2)
log₅ (x-4)> -1
ОДЗ: x-4>0
x>4
x-4> 5⁻¹
x>4+(1/5)
x>4+0.2
x>4.2
x∈(4.2; +∞)
Ответ: (4,2; +∞)
1 votes
Thanks 1
LinaMalik
Log4(2x+3)=log4(4^2)
2x+3=4^2
2x+3=16
2x=13
X=6,5
log5(x-4)>log5(5^-1)
log5(x-4)-log5(5^-1)>0
(5-1)(x-4-1/5)>0
4(x-4-1/5)>0
x-4,2>0
x>4,2
0 votes
Thanks 1
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Answers & Comments
Verified answer
1)log₄ (2x+3)=2
ОДЗ: 2x+3>0
2x> -3
x> -1.5
2x+3=4²
2x+3=16
2x=16-3
2x=13
x=6.5
Ответ: 6,5
2)
log₅ (x-4)> -1
ОДЗ: x-4>0
x>4
x-4> 5⁻¹
x>4+(1/5)
x>4+0.2
x>4.2
x∈(4.2; +∞)
Ответ: (4,2; +∞)
2x+3=4^2
2x+3=16
2x=13
X=6,5
log5(x-4)>log5(5^-1)
log5(x-4)-log5(5^-1)>0
(5-1)(x-4-1/5)>0
4(x-4-1/5)>0
x-4,2>0
x>4,2