Помогите с решением данной системы,пожалуйста )
10-11 класс
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log(x)(2x^-1)*log(x)(2x²)=(log(x)2 -1)*(log(x)2 +2)
log(2x)x*log(2x^-2)x=1/(log(x)2 +1) *1/(log(x)2 -2)=1/(log(x)2 +1) *(log(x)2 -2)
log(x)(2x^-1)*log(x)(2x²)/log(2x)x*log(2x^-2)x=
=(log(x)2 -1)*(log(x)2 +2) :1/(log(x)2 +1) *(log(x)2 -2)=
=(log(x)2 -1)*(log(x)2 +2) * (log(x)2 +1) *(log(x)2 -2)=((log(x)2)² -1)*((log(x)2)² -4)<40
(log(x)2)^4 - 5(log(x)2)² +4-40<0
(log(x)2)^4 - 5(log(x)2)² -36<0
(log(x)2)²=a
a²-5a-36<0⇒a1+a2=5 U a1*a2=-36⇒a1=-4 U a2=9
+ _ +
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-4 9
-4<a<9⇒-4<(log(x)2)²<9
(log(x)2)²>-4 при любом х>0 U x≠1
(log(x)2)²<9⇒(log(x)2)²-9<0
(log(x)2)²=b
b²-9<0⇒(b-3)(b+3)<0
b=-3 U b=3
+ _ +
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-3 3
-3<b<3⇒-3<log(x)2<3⇒1/8<x<8
x∈(1/8;8)