正数等比数列{an}中,a4a5=32,则log2 a1+ log2 a2+……+ log2 a8=

分类: 作业答案 • 2022-03-03 16:20:10

问题描述：

答

a4a5=32=a1^2*Q^7
log2 a1+ log2 a2+……+ log2 a8
=log2 a1*a2*a3*a4*a5*a6*a7*a8
=1og2 a1^8*Q^28
=1og2 32^4
=20

答

a1a8=a2a7=a3a6=a4a5=32
原式=log2(a1a2a3a4a5a6a7a8)=log2(32^4)=log2((2^5)^4)=20

答

由题意,
原式=log2[a1*a2*..*a8]
=log2(a4*a5)^4
=log2(2^20)
=20