等比数列一道题目已知等比数列{an}中,a4a5=16,则log2a1+log2a2+...+log2a8=?

来源:学生作业帮助网 编辑:作业帮 时间:2024/05/01 23:49:31
等比数列一道题目已知等比数列{an}中,a4a5=16,则log2a1+log2a2+...+log2a8=?

等比数列一道题目已知等比数列{an}中,a4a5=16,则log2a1+log2a2+...+log2a8=?
等比数列一道题目
已知等比数列{an}中,a4a5=16,则log2a1+log2a2+...+log2a8=?

等比数列一道题目已知等比数列{an}中,a4a5=16,则log2a1+log2a2+...+log2a8=?
a4a5=a3a6=a2a7=a1a8=16
log2a1+log2a2+...+log2a8
=log2(a1a2a3a4a5a6a7a8)
=log2(16^4)
=log2(2^16)
=16

log2a1+log2a2+...+log2a8=log2(a1*a2……a8)
由于等比数列a1*a8=a2*a7=a3*a6=a4.a5
故所求为log2(16*16*16*16)=4*4=16

a4a5=a1a8=a2a7=a3a6,log2a1 log2a2 … log2a8=log2(a1 a2 …a8〕=16