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\begin{document}


\title{On-line Math 21}


\email{david.johnson@lehigh.edu}


\urladdr{http://www.lehigh.edu/\textasciitilde{}dlj0}

\maketitle

\subsection{Exponential and Logarithmic functions}

\begin{example}
\( 2^{x}=e^{x\, \ln 2} \).
\end{example}

\subsubsection*{Solution}

This one is true because \[
2=e^{\ln 2},\]
so \begin{eqnarray*}
2^{x} &amp; = &amp; \left( e^{\ln 2}\right) ^{x}\\
 &amp; = &amp; e^{x\, \ln 2},
\end{eqnarray*}
again from the rules for exponentiation.
\end{document}
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