对数运算法则之证明

\begin{array}{c}
proof:\quad \log_{a}{x^n}=n\log_{a}{x}\\
设:\log_{a}{x}=m,\quad 即a^m=x\\
则:\log_{a}{x^n} \Rightarrow \log_{a}{(a^m)^n} \Rightarrow \log_{a}{a^{mn}}\\
\because a^m=x,\quad \log_{a}{x}=m\\
\therefore \log_{a}{a^m}=m\\
\therefore \log_{a}{a^{mn}} \Rightarrow mn\\
\because m=\log_{a}{x}\\
\therefore \log_{a}{a^{mn}} \Rightarrow n \times m \Rightarrow n \times \log_{a}{x}\\
\therefore \log_{a}{x^n}=n\log_{a}{x}
\end{array}

标签：log,because,法则,运算,mn,therefore,quad,对数,Rightarrow
来源： https://www.cnblogs.com/Preparing/p/11784979.html