Question

Помогите решить!!! log^2[2](3-x) +log[2]((x-3)^2)<8

Answer 1

ОДз  3-x>0⇒x<3 U x-3≠0⇒x≠3
x∈(-∞;3)
log²(2)(3-x)+log(2)(3-x)²<8
og²(2)(3-x)+2log(2)(3-x)-8<0
log(2)(3-x=a
a²+2a-8<0
a1+a2=-2 U a1*a2=-8⇒a1=-4 U a2=2
-4<a<2⇒-4<log(2)(3-x)<2
1/16<3-x<4
-1/16-3<-x<4-3
-3 1/16<x<1
-1<x<3 1/4 +ОДЗ⇒x∈(-1;3)

Answer 2

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