已知{an}是等比数列,an>0,且a3*a6*a9=4,则log2a2+log2a4+log2a8+log2a10=?a.8b.8/3c.4/3d.4

问题描述:

已知{an}是等比数列,an>0,且a3*a6*a9=4,则log2a2+log2a4+log2a8+log2a10=?
a.8
b.8/3
c.4/3
d.4

log2a2+log2a4+log2a8+log2a10=log2(a2*a4*a6*a8)=log2(a6)^4=4log2a6,a3*a6*a9=a6^3=4,所以log4a6=3,即0.5log2a6=3,所以log2a6=6,所以原式=4*6=24.