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等比数列{an}的各项均为正数且a5a6+a4a7=18,求log3a1+log3a2+...+log3a10的值
人气:290 ℃ 时间:2020-05-09 06:25:10
解答
a5a6+a4a7=18
a5a6+a5a6=18
2a5a6=18
a5a6=9
log3a1+log3a2+...+log3a10
=log3(a1*a2*...*a10)
=log3(a5*a6)^5
=log3 9^5
=log3 (3^2)^5
=log3 3^10
=10
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