第三式证明:https://www.cnblogs.com/Preparing/p/11784979.html
第五式证明:https://www.cnblogs.com/Preparing/p/16057564.html
第六式证明:https://www.cnblogs.com/Preparing/p/16068565.html
\begin{array}{c} 对数运算法则列表: \\ 一: \log_{a}{(\frac{m}{n})} = \log_{a}{m} - \log_{a}{n}\\ \\ 二: \log_{a}{(m \cdot n)} = \log_{a}{m}+\log_{a}{n}\\ \\ 三: \log_{a}{m^n} = n \log_{a}{m}\\ \\ 四: \log_{a}{\frac{1}{n}} = \log_{a}{n^{-1}} = -\log_{a}{n}\\ \\ 五: \log_{a}{b} = \frac{\log_{c}{b}}{\log_{c}{a}}\\ \\ 六: \log_{a^n}{b^m} = \frac{m}{n} {\log_{a}{b}}\\ \\ \end{array}