Question

等比数列，an大于0，a3*a6*a9=4,则log2a2+log2a4+log2a6+log2a8+log2a10=

Answer 1

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

Answer 2

因为a3*a9=(a6)^2
所以(a6)^3 =4
那么log2a2+log2a4+log2a6+log2a8+log2a10=log2 a2*a4*a6*a8*a10=log2 (a6)^5 =5log2 a6=5/3 log2 (a6)^3 =5/3 log2 4=10/3