Помогите , пожалйуста )) (log2 x)^2

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( Log(2) x )² - 4Log(2) x +3 ≤ 0;
( Log(2) x - 1 ) ( Log(2) x - 3 ) ≤ 0 ;
1 ≤ Log(2) x ≤ 3 ;
2 ≤ x ≤ 8 .

ответ: x ∈ [2 ;8] .

* * * * * * * * * * *
P.S. ( Log(2) x )² - 4Log(2) x +3 =0
квадратное уравнение относительно Log(2) x
1 - 4 +3 =0 ⇒ значит Log(2) x =1⇒x =2
второе решение будет Log(2) x =3⇒ x=2³ =8 ..
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Log(2) x= t ;
t² 4t +3 =0 ;
D/4 =2² -3 =1² ;
t₁ =2 - =1;
t₂=2+1 =3 .
(t -1)(t-3) ≤ 0 ;( 1 ≤ t ≤3 - между корнями )
+ - +
------------ [1] ////////////// [3] --------------

1 ≤ loq(2) x ≤ 3

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