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MrKaspian
@MrKaspian
August 2022
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ПОМОГИТЕ решить неравенство:log3(2x+1)-log3(x-1)<log3(x+3) все тройки у логарифмов-основания.
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shevtsovavalia
ОДЗ: 2х+1>0
x-1>0 ⇒x>1
x+3>0
(2x+1)/(x-1)<x+3
(2x+1-x²-2x+3)/(x-1)<0
(-x²+4)/(x-1)<0
f(x)=(-x²+4)/(x-1)
x=2;x=-2;x=1,учитывая ОДЗ f(x)<0; x∈(2;+∞)
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Answers & Comments
x-1>0 ⇒x>1
x+3>0
(2x+1)/(x-1)<x+3
(2x+1-x²-2x+3)/(x-1)<0
(-x²+4)/(x-1)<0
f(x)=(-x²+4)/(x-1)
x=2;x=-2;x=1,учитывая ОДЗ f(x)<0; x∈(2;+∞)