Log<A n > b = log & lta & gtb/n=( 1/n)log<a & gtb.②

Log<A>M log<B>N = log<B>M/log <; b & gta* log & lt； a & gtn/log & lt； a & gtb = log & lta & gtNlog & ltb & gtM.③

By log

A (log<a>N * log<a>m)

=[a^log<； a & gtn^log<； a & gtM

=n^log<； a & gtm，

Similarly, a (log

∴N^logaM=M^logaN ④

Log<N & gtM=(logaM)/(logaN). ⑤

Proof: let m = n b, and then logarithm

∴log<； N & gtM = b = log & lta & gtm/log & lt； A> noun (abbreviation of noun)

(2) With logarithm as exponential power, the base of logarithm and real number can be transposed. See ④.

The product of two logarithms, real numbers are interchangeable. See ③

When the base is the same, the ratio of two logarithms has nothing to do with the base. (changed the topic) See ⑤.