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\Huge{
Logarithmic \& Exponential Equations}
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\noindent
While working in a group make sure you:
\begin{packed_itemize}
\item Expect to make mistakes but be sure to reflect/learn from them!
\item Are civil and are aware of your impact on others.
\item Assume and engage with the strongest argument while assuming best intent.
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\noindent This is a bit of a reminder of \S3.1-3.3 but it will also prime you for \S3.4!
\begin{enumerate}
\item Find the value $t$ in the following by writing logarithmic equations as exponential equations or vice versa.
\begin{enumerate}
\item $18=e^{-.05t}$
\vspace{1.5in}
\item $\log_2(t+2)=5$
\vspace{1.5in}
\item $\log(10^4)=t$
\vspace{1.5in}
\end{enumerate}


\item Write the expressions as a single logarithm or a single exponent:

$4^{5x}\cdot 16^{x^3}$ \hspace{2in} $\log(x-16)+\log(x-1)$

\vspace{2in}


\item Find all $x$ that satisfy:
\begin{enumerate}
\item $2000e^{.05x}=10,000$
\vfill
\item $\log (x-16)=2- \log(x-1)$
%\item $3^{5x}9^{x^2}=27$
\vfill
\item $2\ln(-x)=\ln(36)$
\vfill
\item $\displaystyle{\frac{10}{1+e^{-x}}=2}$
\vfill
\item $\displaystyle{7^{\frac{x}{3}\ln 5}=9}$
\vfill
\item $\log_2(\log_3(x))=4$
\vfill
\end{enumerate}


\end{enumerate}



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