某道对数例题

\begin{array}{c}
若 \log_{18}{9}=a, 18^{b}=5,如何用a,b表示 \log_{36}{45}\\ 
解:\quad \because  \log_{36}{45}=\frac{\log_{18}{45}}{\log_{18}{36}} \\

\log_{18}{45}=\log_{18}{(5 \cdot 9)} \Rightarrow \log_{18}{9}+\log_{18}{5}
\Rightarrow a+b
\\
\log_{18}{36}=\log_{18}{(\frac{36 \cdot 9}{9})}
\Rightarrow 
\log_{18}{(36\cdot9)} - \log_{18}{9}\\
\because \log_{18}{(36\cdot9)} \Rightarrow 
\log_{18}{(4\cdot9\cdot9)}\\
设 \log_{18}{(4\cdot9\cdot9)}=n, 则 18^{n}=2^{2} \cdot 9^{2}\\
得n=2\\
\therefore \log_{36}{45}=\frac{a+b}{2-a} 
\end{array}

标签：某道,log,18,45,36,cdot9,对数,例题,Rightarrow
来源： https://www.cnblogs.com/Preparing/p/16455743.html