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\documentclass[a4paper]{article}
% for dvipdfm:
%\def\pgfsysdriver{pgfsys-dvipdfm.def}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}% <-- moves axis labels near ticklabels (respects tick label widths)
\begin{document}
\begin{figure}
\centering
\begin{tikzpicture}
\begin{loglogaxis}
\addplot coordinates {
(1,1)
(16,16)
(32,64)
};
\end{loglogaxis}
\end{tikzpicture}
\caption{A small example}
\end{figure}
\begin{figure}
\centering
\begin{tikzpicture}
\begin{loglogaxis}[
xlabel=Cost,
ylabel=Error]
\addplot coordinates {
(5, 8.31160034e-02)
(17, 2.54685628e-02)
(49, 7.40715288e-03)
(129, 2.10192154e-03)
(321, 5.87352989e-04)
(769, 1.62269942e-04)
(1793, 4.44248889e-05)
(4097, 1.20714122e-05)
(9217, 3.26101452e-06)
};
\addplot coordinates {
(7, 8.47178381e-02)
(31, 3.04409349e-02)
(111, 1.02214539e-02)
(351, 3.30346265e-03)
(1023, 1.03886535e-03)
(2815, 3.19646457e-04)
(7423, 9.65789766e-05)
(18943, 2.87339125e-05)
(47103, 8.43749881e-06)
};
\legend{Case 1,Case 2}
\end{loglogaxis}
\end{tikzpicture}
\caption{A larger example}
\end{figure}
\end{document}
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