対数
微分に関する公式
d d x ln  x = 1 x {\displaystyle {\frac {d}{dx}}\ln x={\frac {1}{x}}}
d d x log a  x = d d x ln  x ln  a = 1 x ln  a = log a  e x {\displaystyle {\frac {d}{dx}}\log _{a}x={\frac {d}{dx}}{\frac {\ln x}{\ln a}}={\frac {1}{x\ln a}}={\frac {\log _{a}e}{x}}}
マクローリン展開
ln  ( 1 + x ) = ∑ n = 1 ∞ ( − 1 ) n − 1 n x n ( | x | < 1 ) {\displaystyle \ln(1+x)=\sum _{n=1}^{\infty }{\frac {(-1)^{n-1}}{n}}x^{n}\quad (|x|<1)}
ln  ( 1 − x ) = − ∑ n = 1 ∞ 1 n x n ( | x | < 1 ) {\displaystyle \ln(1-x)=-\sum _{n=1}^{\infty }{\frac {1}{n}}x^{n}\quad (|x|<1)}