ОДЗ
{x+4>0⇒x>-4
{4x+16>0⇒4x>-16⇒x>-4
{4x+16≠1⇒4x≠-15⇒x≠-3,75
x∈(-4;3,75) U (-3,75;∞)
log(ab=log(c)a/log(c)b
log(4x+16)8=log(2)8/log(2)(4x+16)
log(4x+16)=3/log(2)[4(x+4)]
log(2)8=3/(2+log2(x+4))
log(2)x=a
a≥3/(a+2)
a-3/(a+2)≥0
(a²+2a-3)/(a+2)≥0
a1+a2=-2 U a1*a2=-3 U a2=1
a+2=0⇒a=-2
_ + _ +
----------------[-3]------------(-2)----------------[1]-------------
-3≤a<-2⇒-3≤log(2)3<-2⇒1/8≤x<1/4<br>a≥1⇒log(2)x≥1⇒x≥2
x∈[1/8;1/4) U [2;∞)