问题 填空题

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

答案

{an}是等比数列,an>0,a3a6a9=a63=4,

∴a6=2

2
3
,即log2(a6)=
2
3

∴log2a2+log2a4+log2a8+log2a10

=log2(a2•a4•a8•a10

=log2(a32•a92

=log2(a64

=4log2(a6

=

8
3

故答案为:

8
3

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