等比数列,an大于0,a3*a6*a9=4,则log2a2+log2a4+log2a6+log2a8+log2a10=
问题描述:
等比数列,an大于0,a3*a6*a9=4,则log2a2+log2a4+log2a6+log2a8+log2a10=
答
易知a3*a9=a6*a6
所以a6*a6*a6=4
而a2*a10=a6*a6
a4*a8=a6*a6
log2a2+log2a4+log2a6+log2a8+log2a10=log2(a2*a10*a4*a8*a6)=a6*a6*a6*a6*a6=10/3