兩正數(shù)的積的對(duì)數(shù),等于同一底數(shù)的這兩個(gè)數(shù)的對(duì)數(shù)的和。兩個(gè)正數(shù)商的對(duì)數(shù),等于同一底數(shù)的被除數(shù)的對(duì)數(shù)減去除數(shù)對(duì)數(shù)的差。一個(gè)正數(shù)冪的對(duì)數(shù),等于冪的底數(shù)的對(duì)數(shù)乘以冪的指數(shù),。若式中冪指數(shù)則有以下的正數(shù)的算術(shù)根的對(duì)數(shù)運(yùn)算法則:一個(gè)正數(shù)的算術(shù)根的對(duì)數(shù),等于被開方數(shù)的對(duì)數(shù)除以根指數(shù)。
對(duì)數(shù)公式是數(shù)學(xué)中的一種常見公式，如果a^x=N(a>0,且a≠1)，則x叫做以a為底N的對(duì)數(shù),記做x=log(a)(N)，其中a要寫于log右下。其中a叫做對(duì)數(shù)的底，N叫做真數(shù)。通常我們將以10為底的對(duì)數(shù)叫做常用對(duì)數(shù)，以e為底的對(duì)數(shù)稱為自然對(duì)數(shù)。
對(duì)數(shù)運(yùn)算法則(rule of logarithmic operations）一種特殊的運(yùn)算方法.指積、商、冪、方根的對(duì)數(shù)的運(yùn)算法則。
由指數(shù)和對(duì)數(shù)的互相轉(zhuǎn)化關(guān)系可得出:兩個(gè)正數(shù)的積的對(duì)數(shù)，等于同一底數(shù)的這兩個(gè)數(shù)的對(duì)數(shù)的和，兩個(gè)正數(shù)商的對(duì)數(shù)，等于同一底數(shù)的被除數(shù)的對(duì)數(shù)減去除數(shù)對(duì)數(shù)的差。
