y=[-loga(a^2x)][-loga^2(ax)] =[2+loga(x)]*1/2[1+loga(x)]2<=x<=4 y最大值为0y=[2+loga(2)]*1/2[1+loga(2)]<=0-2<=loga(2)<=-1若a>1,loga(2)>0,无解若0<a<1,-2<=1/log2(a)<=-1-1<=log2(a)<=-1/21/2<=a<=√2/2[2+loga(4)]*1/2[1+loga(4)]<=0-2<=loga(4)<=-1若a>1,loga(4)>0,无解若0<a<1,-2<=1/log4(a)<=-1-1<=log4(a)<=-1/21/4<=a<=1/2∴a=1/2,y有最大值0y=[2+loga(x)]*1/2[1+loga(x)]=1/2[loga(x)+3/2]^2-1/8当a=1/2,log1/2(x)=-3/2,x=(1/2)^(-3/2)=2√2,y最小值=-1/82√2∈[2,4],符合题意∴a的值为1/2