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(log²(3)x-log(3)x-2)/(log(3)x-1)≤0
log(3)x=a
(a²-a-2)/(a-1)≤0
a²-a-2=0
a1+a2=1 U a1*a2=-2⇒x1=-1 U x2=2
a-1=0⇒a=1
_ + _ +
----------------[-1]----------(1)-------------[2]---------------
a≤-1⇒log(30x≤-1⇒x≤1/3
1<a≤2⇒1<log(3)x≤2⇒3<x≤9
x∈(0;1/3] U (3;9]
lgx=a
(a²-3a+3-a+1)/(a-1)≤0
(a²-4a+4)/(a-1)≤0
(a-2)²/(a-1)≤0
a=2 a=1
_ + +
------------(1)------------[2]-----------------
a<1 ⇒lgx<1⇒x<10 U a=2⇒lgx=2⇒x=100
x∈(0;10) U {100}
log(3)x=a
(a²-a-2)/(a-1)≤0
a²-a-2=0
a1+a2=1 U a1*a2=-2⇒x1=-1 U x2=2
a-1=0⇒a=1
_ + _ +
----------------[-1]----------(1)-------------[2]---------------
a≤-1⇒log(30x≤-1⇒x≤1/3
1<a≤2⇒1<log(3)x≤2⇒3<x≤9
x∈(0;1/3] U (3;9]
lgx=a
(a²-3a+3-a+1)/(a-1)≤0
(a²-4a+4)/(a-1)≤0
(a-2)²/(a-1)≤0
a=2 a=1
_ + +
------------(1)------------[2]-----------------
a<1 ⇒lgx<1⇒x<10 U a=2⇒lgx=2⇒x=100
x∈(0;10) U {100}
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