a>b>0,ab=100,若函数f(x)=lg(x/a)乘以lg(x/b)的最小值为-0.25,求log(以a为第b)

lg(x/a)*lg(x/b)=(lgx-lga)(lgx-lgb)
=(lgx)^2-lgx(lga+lgb)+lgalgb
min=[4lgalgb-(lga+lgb)^2]/4=-[(lga-lgb)^2]/4=-1/4
a>b>0 lga-lgb=1 lg(a/b)=1
所以,lg(b/a)=-1
log(以a为第b)=-1