等比数列【an】的各项均为正数,a5a6+a4a7=18,那么log3 a1+log3 a2……log3 a10=
问题描述:
等比数列【an】的各项均为正数,a5a6+a4a7=18,那么log3 a1+log3 a2……log3 a10=
答
因为4+7=5+6,
所以a4a7=a5a6,
于是由条件知 a5a6=9
所以
log3 a1+log3 a2……log3a10
=log3(a1a2...a10)
=log3[(a1a10)(a2a9)...(a5a6)]
=log3(9^5)
=5log3(9)=10