等比数列｛an｝的各项均为正数,且a5a6+a4a - 知识问答

等比数列｛an｝的各项均为正数,且a5a6+a4a7=18,求图片中式子的值

1个回答

解:
由于{an}为等比数列
则:a5a6=a4a7=a3a8=a2a9=a1a10
又a5a6+a4a7=18
则:
2a5a6=18
a5a6=9
则:
log3(a1)+log3(a2)+...+log3(a9)+log3(a10)
=log3[a1*a2*a3*...*a10]
=log3[(a1a10)*(a2a9)*...*(a5a6)]
=log3[9*9*...*9]
=log3[9^5]
=log3[3^10]
=10log3[3]
=10
祝你学习愉快

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