(log²(2)x-2log(2)x)²-18(log²(2)x-2log(2)x)+45≤0 log²(2)x-2log(2)x=a a²-18a+45≤0 a1+a2=18 U a1*a2=45 a1=3 u a2=15 3≤a≤15 {log²(2)x-2log(2)x≥3 (1) {log²(2)x-2log(2)x≤15 (2) 1)log(2)x=a a²-2a-3≥0 a1=a2=2 U a18a2=-3⇒a1=-1 U a2=3⇒a≤-1 u a≥3 log(2)x≤-1⇒x≤1/2 U log(2)x≥3⇒x≥8 2)a²-2a-15≤a a1+a2=2 U a1*a2=-15⇒a1=-3 U a2=5⇒-3≤a≤5 -3≤log(2)x≤5⇒1/8≤x≤32 x∈[1/8;1/2] U [8;32]
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(log²(2)x-2log(2)x)²-18(log²(2)x-2log(2)x)+45≤0log²(2)x-2log(2)x=a
a²-18a+45≤0
a1+a2=18 U a1*a2=45
a1=3 u a2=15
3≤a≤15
{log²(2)x-2log(2)x≥3 (1)
{log²(2)x-2log(2)x≤15 (2)
1)log(2)x=a
a²-2a-3≥0
a1=a2=2 U a18a2=-3⇒a1=-1 U a2=3⇒a≤-1 u a≥3
log(2)x≤-1⇒x≤1/2 U log(2)x≥3⇒x≥8
2)a²-2a-15≤a
a1+a2=2 U a1*a2=-15⇒a1=-3 U a2=5⇒-3≤a≤5
-3≤log(2)x≤5⇒1/8≤x≤32
x∈[1/8;1/2] U [8;32]