an是等比数列,an>0,且a3a6a9=4,则log2a2+log2a4+log2a8+log2a10=

问题描述:

an是等比数列,an>0,且a3a6a9=4,则log2a2+log2a4+log2a8+log2a10=

a3a6a9=a6^3=4 a6=4^(1/3)
log2a2+log2a4+log2a8+log2a10=log2(a2*a4*a8*a10)=log2(a6^2*a6^2)
=4log2a6=4log2(4^(1/3))=8/3