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\begin{frame}
  \frametitle{Natural Logarithm}
  
  \begin{block}{}
    The \emph{natural logarithm} $\ln$ is a special logarithm with base $e$:
    \begin{talign}
      \ln x = \log_e x
    \end{talign}
  \end{block}
  \pause
  
  \begin{exampleblock}{}
    Solve the equation $e^{5-3x} = 10$.\pause
    \begin{talign}
      \ln (e^{5-3x}) &= \ln 10 &&\text{apply natural logarithm on both sides}\\
      \mpause[1]{5-3x} &\mpause[1]{= \ln 10} \\
      \mpause[2]{3x} &\mpause[2]{= 5 - \ln 10} \\
      \mpause[3]{x} &\mpause[3]{= \frac{5 - \ln 10}{3}}
    \end{talign}
  \end{exampleblock}
  \pause\pause\pause\pause
  
  \begin{exampleblock}{}
    Express $\ln a + \frac{1}{2} \ln b$ in a single logarithm.\pause
    \begin{talign}
      \ln a + \frac{1}{2} \ln b
      &\mpause[1]{= \ln a + \ln b^{\frac{1}{2}}} 
      \mpause[2]{= \ln a + \ln \sqrt{b}} 
      \mpause[3]{= \ln (a\sqrt{b})}
    \end{talign}
  \end{exampleblock}
\end{frame}