\documentclass{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.12}
\begin{document}
\begin{tikzpicture}
\begin{loglogaxis}[name=first,domain=1:1000,axis lines=left,
enlargelimits=0.2,log ticks with fixed point,xlabel={$x$},ylabel={$y$},
ylabel style={at={(0,1)}, anchor=south,rotate=-90},
xlabel style={at={(1,0)}, anchor=west},
]
\addplot[only marks] {rand};
\end{loglogaxis}
\begin{loglogaxis}[at={(first.south west)},
anchor=south east,hide y axis,domain=1:1000,axis x line=bottom,x dir=reverse,
enlargelimits=0.2,log ticks with fixed point,xlabel={$x$},
xlabel style={at={(0,0)}, anchor=east},
]
\addplot[only marks] {rand};
\end{loglogaxis}
\end{tikzpicture}
\end{document}