Question

log a b*log b c=log b b*log a c成立吗

Answer 1

用换底公式,

左边

=log a b*log b c

=(lg b/lg a)*(lg c/lg b)

=lg c/lg a

=loga c

右边

=log b b*log a c

=1*log a c

=loga c

左边=右边

所以,log a b*log b c=log b b*log a c成立