  We explore the evolution of the X-ray luminosity function of quasars and the
intrinsic correlation between the X-ray and 2500\AA $\,$ ultraviolet
luminosities, utilizing techniques verified in previous works and a sample of
over 4000 quasars detected with Chandra and XMM-Newton in the range $0<z<5$. We
find that quasars have undergone significantly less evolution with redshift in
their total X-ray luminosity than in other wavebands. We then determine that
the best fit intrinsic power law correlation between the X-ray and ultraviolet
luminosities, of the form $L'_{\rm X} \propto ({L'_{\rm UV}})^{\gamma}$, is
$\gamma=0.28\pm$0.03, and we derive the luminosity function and density
evolution in the X-ray band. We discuss the implications of these results for
models of quasar systems.
