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Cosmography is a powerful tool to investigate the Universe kinematic and then to reconstruct dynamics in a model-independent way. However, recent new measurements of supernovae Ia and quasars have populated the Hubble diagram up to high redshifts ($z \sim 7.5$) and the application of the traditional cosmographic approach has become less straightforward due to the large redshifts implied. Here we investigate this issue through an expansion of the luminosity distance-redshift relation in terms of "orthogonal" logarithmic polynomials. In particular we point out the advantages of a new procedure of "orthogonalization" and we show that such an expansion provides a very good fit in the whole $z=0\div 7.5$ range to both real and mock data obtained assuming various cosmological models. Moreover, despite of the fact that the cosmographic series is tested well beyond its convergence radius, the parameters obtained expanding the luminosity distance - redshift relation for the $\Lambda$CDM model are broadly consistent with the results from a fit of mock data obtained with the same cosmological model. This provides a method to test the reliability of a cosmographic function to study cosmological models at high redshifts and it demonstrates that the logarithmic polynomial series can be used to test the consistency of the $\Lambda$CDM model with the current Hubble diagram of quasars and supernovae Ia. We confirm a strong tension (at $>4\sigma$) between the concordance cosmological model and the Hubble diagram at $z>1.5$. Such a tension is dominated by the contribution of quasars at $z>2$ and starts to be present also in the few supernovae Ia observed at $z>1$., Comment: 11 pages, 7 figures, accepted for publication in A&A, comments are welcome

We present a new catalogue of ~2,400 optically selected quasars with spectroscopic redshifts and X-ray observations from either Chandra or XMM-Newton. The sample can be used to investigate the non-linear relation between the UV and X-ray luminosity of quasars, and to build a Hubble diagram up to redshift z~7.5. We selected sources that are neither reddened by dust in the optical/UV nor obscured by gas in the X-rays, and whose X-ray fluxes are free from flux-limit related biases. After checking for any possible systematics, we confirm, in agreement with our previous works, that (i) the X-ray to UV relation provides distance estimates matching those from supernovae up to z~1.5, and (ii) its slope shows no redshift evolution up to z~5. We provide a full description of the methodology for testing cosmological models, further supporting a trend whereby the Hubble diagram of quasars is well reproduced by the standard flat $\Lambda$CDM model up to z~1.5-2, but strong deviations emerge at higher redshifts. Since we have minimized all non-negligible systematic effects, and proven the stability of the $L_{\rm X}-L_{\rm UV}$ relation at high redshifts, we conclude that an evolution of the expansion rate of the Universe should be considered as a possible explanation for the observed deviation, rather than some systematic (redshift-dependent) effect associated with high-redshift quasars., Comment: 24 pages, 17 figures, accepted for publication in A&A