lg5的平方+lg2乘lg50 和里面的一题第一:lg5的平方+lg2乘lg50第二:(log以2为底125+log以4为底25+log以8为底5) 乘(log以125为底8+log以25为底4+log以5为底2)
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lg5的平方+lg2乘lg50 和里面的一题第一:lg5的平方+lg2乘lg50第二:(log以2为底125+log以4为底25+log以8为底5) 乘(log以125为底8+log以25为底4+log以5为底2)
lg5的平方+lg2乘lg50 和里面的一题
第一:lg5的平方+lg2乘lg50
第二:(log以2为底125+log以4为底25+log以8为底5) 乘(log以125为底8+log以25为底4+log以5为底2)
lg5的平方+lg2乘lg50 和里面的一题第一:lg5的平方+lg2乘lg50第二:(log以2为底125+log以4为底25+log以8为底5) 乘(log以125为底8+log以25为底4+log以5为底2)
(1)(lg5)^2+lg2*lg50=(lg5)^2+lg2*(lg25+lg2)=(lg5)^2+lg2*(2lg5+lg2)
=(lg)^2+2lg2*lg5+(lg2)^2=(lg5+lg2)^2=(lg10)^2=1
(2)log以2为底125表示成log(2)(125),其他类推
[log(2)(125)+log(4)(25)+log(8)(5)]*[log(125)8+log(25)4+log(5)(2)]
=[3log(2)(5)+log(2)5+(1/3)log(2)(5)]*[log(5)(2)+log(5)(2)+log(5)(2)]
=(13/3)*log(2)(5)*3log(5)(2)=13
(lg5)^2 +lg2 *lg50 = (lg5)^2 +lg(10/5) *lg(5*10)
=(lg5)^2 +( lg10 -lg5) * (lg10 +lg5)
=(lg5)^2 + (1-lg5) (1+lg5)
=1
[log(2,125) + log(4,25) +log(8,5)] * [log(125, 8) + log (25, 4)+log(...
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(lg5)^2 +lg2 *lg50 = (lg5)^2 +lg(10/5) *lg(5*10)
=(lg5)^2 +( lg10 -lg5) * (lg10 +lg5)
=(lg5)^2 + (1-lg5) (1+lg5)
=1
[log(2,125) + log(4,25) +log(8,5)] * [log(125, 8) + log (25, 4)+log(5,2)]
=[ 3log(2, 5) + log (2, 5) + log(2,5)/3] *[ log(5,2) + log(5,2)/2 +log(5,2)]
=(13/3) * log(2,5) * 3* log(5,2)
=13
第二题利用二个公式: log( a^n, b^m) = (m/n) *log( a,b)
log(a,b) * log(b,a) =1 (换底公式)
其中:log(a,b)是以a为底的b 的对数
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