Question

幂函数 (27 16:32:49)

Answer 1

y=㏒1/a(a2x)×㏒a2（1/ax)

y=㏒a(a2x)·㏒a2(ax)

=[㏒a(a2)+㏒a(x)]·[㏒a2(a)+㏒a2(x)]

=[2+㏒a(x)]·[0.5+0.5㏒a(x)]

设㏒a(x)=m,则

y=(2+m)(0.5+0.5m)=0.5m^2+1.5m+2

当y=-1/8,m=-1.5

当y=0,m1=-1,m2=-2

即㏒a(x)∈[-2,-1]

因为x∈[2,4],㏒a(x)取负值(递减),所以

㏒a(2)=-1

㏒a(4)=-2

所以a=1/2