(log2^5+log4^125)(log5^4+log25^64)
展开全部
(log2 5+log4 125)(log5 4+log25 64)
=(lg5/lg2+lg125/lg4)(lg4/lg5+lg64/lg25)
=[(lg5*lg4+lg125*lg2)/(lg2*lg4)]*[(lg4*lg25+lg64*lg5)/(lg5*lg25)]
因为lg4=2lg2,lg25=2lg5,lg125=3lg5,lg64=6lg2
所以上式变为
=[(2lg5*lg2+3lg5*lg2)/(2lg2*lg2)]*[(4lg2*lg5+6lg2*lg5)/(2lg5*lg5)]
=[(2+3)/2](lg5/lg2)*[(4+6)/2] (lg2/lg5)
=25/2
=(lg5/lg2+lg125/lg4)(lg4/lg5+lg64/lg25)
=[(lg5*lg4+lg125*lg2)/(lg2*lg4)]*[(lg4*lg25+lg64*lg5)/(lg5*lg25)]
因为lg4=2lg2,lg25=2lg5,lg125=3lg5,lg64=6lg2
所以上式变为
=[(2lg5*lg2+3lg5*lg2)/(2lg2*lg2)]*[(4lg2*lg5+6lg2*lg5)/(2lg5*lg5)]
=[(2+3)/2](lg5/lg2)*[(4+6)/2] (lg2/lg5)
=25/2
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