f(x)=lg(x/a)*lg(x/b)
=(lgx-lga)(lgx-lgb)
=(lgx)^2-(lga+lgb)lgx+lga*lgb
=(lgx)^2-(lg ab)lgx+lga*lgb
=(lgx)^2-lg100*lgx+lga*lgb
=(lgx)^2-2lgx+lga*lgb
=(lgx)^2-2lgx+1-1+lga*lgb
=(lgx-1)^2-1+lga*lgb
f(x)的最小值是lga*lgb-1=-1/4
lga*lgb=3/4
log a (a)/loga (10)*loga (b)/loga(10)=3/4
loga (b)=3/4(loga 10)^2