\chapter{Exponentials and logarithms}
\section{Logarithms }
Answer the questions in your own words.
\begin{enumerate}
\item Explain what \(\log_a x\) is.
\item
What is the difference between \(\log_3 x\), \(\log x\) and \(\ln x\)?
\item
The following logarithms can all be found without a calculator, except one. Which one?
\[
\begin{array}{ccccc}
\mbox{(a) } \log_2 32 & \hspace{1ex} \mbox{(b) } \displaystyle\log \frac{1}{10}
& \hspace{1ex}
\mbox{(c) } \ln\sqrt{e} & \hspace{1ex} \mbox{(d) } \log_2 10 & \hspace{1ex} \mbox{(e) }
\log_3 1
\end{array}
\]
\item
The following logarithms can all be found without using the change of base formula,
except one. Which one?
\[
\begin{array}{ccccc}
\mbox{(a) } \log 32 \hspace{1ex} & \mbox{(b) } \displaystyle\log_2 \frac{1}{8}
& \hspace{1ex} \mbox{(c) } \log_5 15
& \hspace{1ex} \mbox{(d) } \ln 3 & \hspace{1ex} \mbox{(e) } \log_9 81
\end{array}
\]
\item Suppose \(x\) is a number greater than \(1\). Arrange the following in increasing order:
\[ \begin{array}{cccc}
\mbox{(a)} \log_2 x \hspace{1ex} & \mbox{(b)} \displaystyle\log x &
\hspace{1ex} \mbox{(c)} \log_5 x & \hspace{1ex} \mbox{(d)} \ln x
\end{array}
\]
\end{enumerate}