log a b*log b c=log b b*log a c成立吗

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