\chapter{Exponentials and logarithms}
\section{Properties of logarithms and logarithmic functions}
Answer the questions.
\begin{enumerate}
\item Suppose you want to simplify \[\ln \left(xy^2\right).\]
Which of the following is the right answer?
\begin{enumerate}
\item
\(2\ln(xy)\)
\item
\(\ln x + 2 \ln y\)
\end{enumerate}
\item
We want to condense the expression into a single quantity:
\[\log (x+2) -\log (x-2).\]
Which of the following is the right answer?
\begin{enumerate}
\item
\(\displaystyle \log \left(\frac{x+2}{x-2}\right)\)
\item
\( \displaystyle \frac{\log(x+2)}{\log(x-2)}\)
\end{enumerate}
\item
Answer True or False:
\begin{enumerate}
\item
\(\log x \) can never be zero.
\item
\(\ln x \) can never be a whole number.
\item
\(\log_3 1=3\)
\item
\(\log_4 2 =2\)
\item
\(\log_3 0 =1\)
\end{enumerate}
\item
Expand \(\displaystyle \ln\left(\frac{x}{yz}\right)\). Which of the following is the right answer?
\begin{enumerate}
\item
\(\ln x - \ln y - \ln z\)
\item
\(\ln x -\ln y +\ln z\)
\end{enumerate}
\end{enumerate}