Question

(log2 5+log4 1/5)(log5 2+log25 1/2)

Answer 1

全部化成以10为底的对数
log2 5=lg2/lg5,
log4 1/5=1g4/lg1/5,
log5 2=lg5/lg2,
log25 1/2=lg25/lg1/2
(log25+log4 1／5)(log5 2+log25 1／2)
=[(lg5／lg2)+(lg1/5／lg4)] [(lg2／lg5)+(lg1/2 ／lg25)]
=[(lg5／lg2)+(lg1/5／lg2^2)] [(lg2／lg5)+(lg1/2／lg5^5)]
=[(lg5／lg2)+(lg1/5／2lg2) ] [(lg2／lg5)+(lg1/2 ／5lg5)]
=(lg5／lg2)*(lg2／lg5)+(lg5／lg2)*(lg1/2 ／5lg5)+(lg1/5／2lg2)*(lg2／lg5)+(lg1/5／2lg2)*(lg1/2 ／5lg5)
=1-1/2-1/2+1/4