y=(loga(a^2)+loga(x))*(loga (a)+loga (x))
=(2+loga(x))*(1+loga(x))
= (loga(x))^2+3loga(x)+2
令t=loga(x)
则y=t^2+3t+2=(t+3/2)² -1/4,为t的二次函数,
t=-3/2时,y=-1/4.
t=-1或-2时,y=0.
画出y--t图象,图象开口向上,当-1/4≤y≤0时,-2≤t≤-1
所以当值域是[-1/4,0]时,定义域是[-2,-3/2],或[-3/2,-1],或[-2,-1].
下面分情况讨论：
1．a>1时,X∈[2,4],则t= loga(x)∈[loga(2),loga(4)]
①[loga(2),loga(4)]= [-2,-3/2],此时无解.
②[loga(2),loga(4)]= [-3/2,-1],此时无解.
③[loga(2),loga(4)] =[-2,-1],此时无解.
2.0