\documentclass{article}
% translate with >> pdflatex -shell-escape <file>

% This file is an extract of the PGFPLOTS manual, copyright by Christian Feuersaenger.
% 
% Feel free to use it as long as you cite the pgfplots manual properly.
%
% See
%   http://pgfplots.sourceforge.net/pgfplots.pdf
% for the complete manual.
%
% Any required input files (for <plot table> or <plot file> or the table package) can be downloaded
% at
% http://www.ctan.org/tex-archive/graphics/pgf/contrib/pgfplots/doc/latex/
% and
% http://www.ctan.org/tex-archive/graphics/pgf/contrib/pgfplots/doc/latex/plotdata/

\usepackage{pgfplots}
\pgfplotsset{compat=newest}

\pagestyle{empty}

\usepackage{pgfplotstable}
\usepackage{array}
\usepackage{colortbl}
\usepackage{booktabs}
\usepackage{eurosym}
\usepackage{amsmath}
\usepackage{pgfplotstable}

\begin{document}
\pgfplotstablenew[
	create on use/cut/.style={create col/function graph cut y=
		{2.5e-4} % search for fixed L2 = 2.5e-4
		{x=Basis,y=L2,ymode=log,xmode=log} % double log, each function is L2(Basis)
		% now, provide each single function f_i(Basis):
		{{table=plotdata/newexperiment1.dat},{table=plotdata/newexperiment2.dat}}
	},
	columns={cut}]
	{2} 
	\loadedtable

% Show the data:
\pgfplotstabletypeset{\loadedtable}

\begin{tikzpicture}
\begin{loglogaxis}
	\addplot table[x=Basis,y=L2] {plotdata/newexperiment1.dat};
	\addplot table[x=Basis,y=L2] {plotdata/newexperiment2.dat};
	\draw[blue!30!white] (axis cs:1,2.5e-4) -- (axis cs:1e5,2.5e-4);
	\node[pin=-90:{$x=53.66$}] at (axis cs:53.66,2.5e-4) {};
	\node[pin=45:{$x=601.83$}] at (axis cs:601.83,2.5e-4) {};
\end{loglogaxis}
\end{tikzpicture}
\end{document}
