等比数列{an}的各项均为正数,且a2a9=9,则log3a1+log3a2+log3a3+···+log3a10=

问题描述:

等比数列{an}的各项均为正数,且a2a9=9,则log3a1+log3a2+log3a3+···+log3a10=

等比数列中,a2a9=a1a10=a3*a8=a4*a7=a5*a6=9
log3a1+log3a2+log3a3+···+log3a10
=log3(a1*a2*a3*.*a10)
=log3(a1a10*a2a9*a3*a8*a4a7*a5a6)
=log3(9^5)
=log3(3^10)
=10
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