지수함수 로그함수 정리

지수함수 정리

$$a^0 = 1$$

$$a^m a^n = a^{m+n}$$

$$(a^m)^n = a^{mn}$$

$$\frac{a^m}{a^n} = a^{m-n}$$

$$(ab)^n = a^n b^n$$

$$(\frac{a}{b})^n = \frac{a^n}{b^n}$$

$$a^{-n} = \frac{1}{a^n}$$

$$\sqrt[n]{a} = a^{\frac{1}{n}}$$

$$\sqrt[n]{a^m} = a^{\frac{m}{n}}$$

 

로그함수 정리

기본정의

$$a^x = c     \implies     \log_{a}{x} = b$$

$$\log_{a}{1} = 0 \text{, }\text{ }\text{ }\text{ } \log_{a}{a} = 1$$

$$\log_{a}{mn} = \log_{a}{m} + \log_{a}{}n$$

$$\log_{a}{\frac{m}{n}} = \log_{a}{m} - \log_{a}{n}$$

$$\log_{a}{M^k} = k\log_{a}{M}$$

$$\log_{a}{M} = \frac{ \log_{b}{M} } { \log_{b}{a} }  \text{ }\text{ } where \text{ }\text{ } a > 0, a \ne 1 \text{ }\text{ }\text{ }\text{ }  b > 0, b \ne 1 \text{ }\text{ }\text{ }\text{ }   M > 0$$

$$\log_{a}{b} = \frac{1}{\log_{b}{a}}$$

$$a^{\log_{a}{b}} = b$$

$$a^{\log_{b}{c}} = c^{\log_{b}{a}}$$