設(shè)x＝a^m,a＝b^n,則
x＝(b^n)^m＝b^(mn)……………………①
對(duì)①取以a為底的對(duì)數(shù),有：
log(a,x)＝m……………………………②
對(duì)①取以b為底的對(duì)數(shù),有：
log(b,x)＝mn……………………………③
③/②,得：
log(b,x)/log(a,x)＝n＝log(b,a)
∴l(xiāng)og(a,x)＝log(b,x)/log(b,a)
注：log(a,x)表示以a為底x的對(duì)數(shù)