等比数列{an}中,an>0,a3*a4=4,则log2a1+log2a2+.log2a6=?

问题描述:

等比数列{an}中,an>0,a3*a4=4,则log2a1+log2a2+.log2a6=?

a3a4=(a1q)²(a1q³)=a1²q^5=4
log2(a1)+log2(a2)+...+log2(a6)
=log2(a1·a2·...·a6)
=log2(a1^6q^15)
=log2[(a1²q^5)³]
=3log2(4)
=3×2
=6