各项为正整的等比数列[An].a4*a7=8则log2*a1+log2*a2+.log2*a10=?
问题描述：
各项为正整的等比数列[An].a4*a7=8则log2*a1+log2*a2+.log2*a10=?
答
a4*a7=8
a1*q^3*a1*q^6=8
a1^2 *q^9=8
log2*a1+log2*a2+.log2*a10
=log2 (a1*a2*...*a10)
=log2 (a1^10 * q^45)
=log2 (a1^2 * q^9)^5
=5log2 8
=5*3
=15