对数计算(Log2为底5的对数+Log4为底125的对数)(Log5为底4的对数+LOg25为底64的对数)=

Question

对数计算
(Log2为底5的对数+Log4为底125的对数)(Log5为底4的对数+LOg25为底64的对数)=

Answer 1

(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]*[(4+6)/2]
=25/2