已知log a1b1=log a2b2=…=log anbn，求证log a1a2…an（b1b2…bn）=log a1b1=log a2b2=…=log anbn．
问题描述：
已知log a1b1=log a2b2=…=log anbn，求证log a1a2…an（b1b2…bn）=log a1b1=log a2b2=…=log anbn．
答
证明：令log a1b1=log a2b2=…=log anbn=N，则lgb1lga1＝lgb2lga2＝…＝lgbnlgan＝N，由分式的合比性质得：lgb1+lgb2+…+lgbnlga1+lga2+…+lgan＝N，即lg(b1b2…bn)lg(a1a2…an)＝N，∴log a1a2...