对数的计算log23×log35×log58=?log259×log27625=?已知log163=m,试用m表示log916

Question

对数的计算
log2 3×log3 5×log5 8=?
log25 9×log27 625=?
已知log16 3=m,试用m表示log9 16

Answer 1

log2 3×log3 5×log5 8
=lg3/lg2*lg5/lg3*lg8/lg5
=lg8/lg2
=3lg2/lg2
=3
log25 9×log27 625
=lg9/lg25*lg625/lg27
=2lg3/2lg5*4lg5/3lg3
=4/3
m=log16 3=lg3/lg16
lg16/lg3=1/m
log9 16=lg16/lg9=lg16/2lg3=1/2m