已知{an}为等比数列an>0且a2a9=81,则以3为底a1的对数+以3为底a2的对数+……+以3为底a9的对数+以3为底a10=?
问题描述：
已知{an}为等比数列an>0且a2a9=81,则以3为底a1的对数+以3为底a2的对数+……+以3为底a9的对数+以3为底a10=?
答
log3 (a1)+log3 (a2)+.+log3 (a10)
=log3 (a1*a2*.*a10)
=log3 (a2*a9)^2
=log3 (81^2)
=log3 (3^8)
=8答案等于20log3 (a1)+log3 (a2)+.......+log3 (a10)=log3 (a1*a2*.......*a10)=log3 (a2*a9)^5（刚才这里错了，不好意思）=log3 (81^5)=log3 (3^20)=20