(Loq_(3-x) (4x -5)*Loq_(4x) (Loq_(2) (7) - x))/cos(π+x)≥0 ;
(Loq_(3-x) (4x -5)*Loq_(4x) (Loq_(2) (7) - x))/cosx ≤ 0 ; [ cos((π+x) = - cosx ] .
ООФ :
{3 - x > 0; 3 -x ≠ 1 ; 4x -5 >0 ; 4x > 0 ; 4x ≠ 1; Loq (_2) - 1> 0 ; x ≠ π/2+π*k , k∈Z.
⇔x∈( 5/4 ;π/2) U (π/2 ; 2) U (2 ; Loq(_2) 7) .
+ - + - -
--- 5/4 ---- Loq_(2) (7/2) -------- 3/2-------- π/2 ------2 ------Loq_(2) 7
x∈ (Loq_(2) (7/2 ; 3/2] U (π/2 ; 2) U (2 ;Loq_(2) 7] .
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Loq_(3-x) (4x -5) = 0 ⇒ 4x -5 =1 ⇔x =3/2 .
Loq_(4x) (Loq_(2) (7) - x) = 0 ⇒ Loq_(2) (7) - x =1
⇔ x = Loq_(2) (7) -1 =Loq_(2) (7) - Loq_(2) (2) = Loq_(2) (7/2).