ОДЗ
{2x²-x>0⇒x(2x-1)>0⇒x<0 U x>1/2
{x+4>0⇒x>-4
{x+4≠1⇒x≠-3
x∈(-4;-3) U (-3;0) U (1/2;∞)
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log(2)[(x+4)^log(2)(2x²-x))≤log(2)(2x²-x)
log(2)(x+4)*log(2)(2x²-x)-log(2)(2x²-x)≤0
log(2)(2x²-x)*(log(2)(x+4)-1)≤0
1){log(2)(2x²-x)≥0
{log(2)(x+4)-1≤0
{(2x²-x)≥1⇒2x²-x-1≥0 D=1+8=9 x1=-1/2 U x2=1⇒x≤-1/2 U x≥1
{log(2)(x+4)≤1⇒x+4≤2⇒x≤-2
x≤-2
x∈(-4;-3) U (-3;-2]
2){log(2)(2x²-x)≤0
{log(2)(x+4)-1≥0
{-1/2≤x≤1
{x≥-2
-1/2≤x≤1
x∈[-1/2;0) U (1/2;1]
Ответ x∈(-4;-3) U (-3;-2] U [-1/2;0) U (1/2;1]