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Proof of Mathematical Formula in Senior High School
( 1)log & lt; n^m>; m^n=log<; N & gtm^n/m=(n/m)log<; N & gtm,①

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.