www.1862.net > 若等比数列An满足log3A1 log3A2......... log3A10=...

若等比数列An满足log3A1 log3A2......... log3A10=...

a5a6=a7a4=a8a3=…=a1a10,a1a2a3a4a5a6a7a8a9a10=(a5a6)的5次方=3的10次方,结果等于10,

解答: 这个是对数的运算法则 同底对数相加,底数不变,真数相乘, 即 loga(M)+loga(N)=loga(MN) 可以推广到有限多个。

因为An是等比数列 所以A1*A10=A2*A9=A3*A8=A4*A7=A5*A6=9 log3 A1+log3A2+。。。。。+log3A10=(log3A1+log3A10)+(log3A2+log3A9)+.....+(log3A5+log3A6)=log3(A1*A10)+....log3(A5*A6)=5*log3(A5*A6)=10

a5=a1q^4 q^4=2^4 q=2 sn=36(2^n-1) log3a1+log3a2+…+log3a10=20 log3a1a2a3……a10=20 log3(a5a6)^5=20 log3(a5a6)=4 a5a6=3^4=81

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...

+log3a9+log3a10等于 等比数列{an}中a2a9=3,则log3a1+log3a2+…+log3a9+log3a10等于?... 等比数列{an}中a2a9=3,则log3a1+log3a2+…+log3a9+...

∵等比数列{an}中,an>0,a5a6=9,∴a1?a2…a10=(a5?a6)5=310,∴log3a1+log3a2+…+log3a10=log3310=10.故选B.

log3a1+log3a2+…+log3a10=log3(a1a10)+log3(a2a9)+…log3(a5a6)=5log3(a5a6)=10故答案为:10

由题意知,a1xa10=a2xa9=a3xa8=a4xa7=a5xa6=9 log3 a1+log3 a2+.......+log3 a10=( log3 a1+log3 a10)+(log3 a2+log3 a9)+(log3 a3+log3 a8)+(log3 a4+log3 a7)+(log3 a5+log3 a6)= log3( a1xa10)+log3( a2xa9)+log3( a3xa8)+lo...

LZ应该知道这条公式吧: lga+lgb=lg(ab) 所以你的问题不难,如果要分步做的话就是: 1、log3a1+log3a2=log3(a1*a2) 2、log3(a1*a2)+log3a3=log3[(a1*a2)*a3]=log3(a1*a2*a3) ..... 以此类推 得到log3a1+log3a2+log3a3+...+log3a10=log3(a1*...

网站地图

All rights reserved Powered by www.1862.net

copyright ©right 2010-2021。
www.1862.net内容来自网络,如有侵犯请联系客服。zhit325@qq.com