{an}是等比数列,an>0,a3a6a9=4,则log2a2+log2a4+log2a8+log2+a10=______.-数学

题目简介

{an}是等比数列,an>0,a3a6a9=4,则log2a2+log2a4+log2a8+log2+a10=______.-数学

题目详情

{an}是等比数列,an>0,a3a6a9=4,则log2a2+log2a4+log2a8+log2+a10=______.
题型:填空题难度:中档来源:不详

答案

{an}是等比数列,an>0,a3a6a9=a63=4,
∴a6=2class="stub"2
3
,即log2(a6)=class="stub"2
3

∴log2a2+log2a4+log2a8+log2a10
=log2(a2•a4•a8•a10)
=log2(a32•a92)
=log2(a64)
=4log2(a6)
=class="stub"8
3

故答案为:class="stub"8
3

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