SIMPLY (log10x)^2 - 2[log10 - (log x)^2] + (log(x/10))^2
Is answer 4(log x)^2 ?
if not, plz tell me the steps and answer, thz~
SIMPLY (log10x)^2 - 2[log10 - (log x)^2] + (log(x/10))^2
2007-03-11 2:44 am
回答 (2)
2007-03-11 4:16 am
(log10x)^2 - 2[log10 - (log x)^2] + (log(x/10))^2
=(log 10+log x)^2-2[1-(log x)^2]+(log x-log 10)^2
=(1+log x)^2 -2 +2(log x)^2+(log x-1)^2
let a= log x
(1+a)^2-2+2a^2+(a-1)^2
=1+2a+a^2-2+2a^2+a^2-2a+1
=a^2+2a^2+a^2+2a-2a+1-2+1
=4a^2
=4(log x)^2
=(log 10+log x)^2-2[1-(log x)^2]+(log x-log 10)^2
=(1+log x)^2 -2 +2(log x)^2+(log x-1)^2
let a= log x
(1+a)^2-2+2a^2+(a-1)^2
=1+2a+a^2-2+2a^2+a^2-2a+1
=a^2+2a^2+a^2+2a-2a+1-2+1
=4a^2
=4(log x)^2
2007-03-11 3:05 am
(log10x) (log(x/10) )
= (log10 + logx)(logx - log10)
= (logx+1)(logx-1)
= (logx)^2 - 1^2
= - (1 - (logx)^2 )
= - [log10 - (logx)^2 ]
(log10x)^2 - 2[log10 - (log x)^2] + (log(x/10))^2
= (log10x)^2 + 2(log10x) [log(x/10)] + (log(x/10))^2
= [log10x + log(x/10)]^2
= [log(10x)(x/10)]^2
= (logx^2)^2
= (2logx)^2
= 4(logx)^2
= (log10 + logx)(logx - log10)
= (logx+1)(logx-1)
= (logx)^2 - 1^2
= - (1 - (logx)^2 )
= - [log10 - (logx)^2 ]
(log10x)^2 - 2[log10 - (log x)^2] + (log(x/10))^2
= (log10x)^2 + 2(log10x) [log(x/10)] + (log(x/10))^2
= [log10x + log(x/10)]^2
= [log(10x)(x/10)]^2
= (logx^2)^2
= (2logx)^2
= 4(logx)^2
收錄日期: 2021-04-12 23:26:33
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20070310000051KK03797