Solution set of the inequality log0.8(log6x2+xx+4)<0
(−4,−3)∪(8,∞)
Since, the base of log0.8(log6x2+xx+4)<0
is less than 1,
log6(x2+xx+4)>1⇒x2+xx+4>6⇒x2+xx+4−6>0
⇒x2+x−6x−24(x+4)>0⇒(x−8)(x+3)(x+4)>0,x≠−4.
⇒−4<x<−3 or x>8.
Thus, required solution set is (−4,−3)∪(8,∞)