решите пожалуйста log1/3 (x-2)>1/(log1/3 (x-2))+3/2. Created by egorvas77. matematika-ru

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egorvas77 @egorvas77

July 2022 1 7 Report

решите пожалуйста
log1/3 (x-2)>1/(log1/3 (x-2))+3/2

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sedinalana

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ОДЗ
x-2>0⇒x>2
log(1/3)(x-2)=a
a>1/a+3/2
(2a²-2-3a)/a>0
2a²-3a-2=0
D=9+16=25
a1=(3-5)/4=-1/2
a2=(3+5)/4=2
a<-1/2⇒log(1/3)(x-2)<-1/2⇒x-2>√3⇒x>2+√3
a>2⇒log(1/3)(x-2)>2⇒x-2<1/9⇒x<2 1/9
x∈(2;2 1/9) U (2+√3;∞)

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