等比数列{an}的各项都为正数,且a5a6+a4a7=18,log3a1+loga2+...+log3a10等于_数学解答

等比数列{an}的各项都为正数,且a5a6+a4a7=18,log3a1+loga2+...+log3a10等于

人气：396 ℃　时间：2020-10-01 19:47:28

解答

因为数列是等比数列,a5a6=a4a7
a5a6+a4a7=2a5a6=18
a5a6=9
a1a10=a2a9=...=a5a6=9
log3 a1+log3 a2+...+log3 a10
=log3 (a1a2a3...a10)
=log3 (a5a6)＾5
=5log3 a5a6
=5×2
=10