Damghan University Press Journal of Holography Applications in Physics 2783-4778 6 4 2026 05 30 Testing Logarithmic f(G) Model with Observational Data Sets 185 216 2098 10.22128/jhap.2026.3248.1191 EN Mohit Thakre Symbiosis Institute of Technology, Nagpur Campus, Symbiosis International, Deemed University, Pune-440008, Maharashtra, India Praveen Kumar Dhankar Symbiosis Institute of Technology, Nagpur Campus, Symbiosis International, Deemed University, Pune-440008, Maharashtra, India 0000-0002-8201-6019 Albert Munyeshyaka Rwanda Astrophysics Space and Climate Science Research Group, University of Rwanda, College of Science and Technology, Kigali, Rwanda 0000-0002-9036-7185 Safiqul Islam Department of Mathematics and Statistics, College of Science, King Faisal University, P.O. Box 400, Al Ahsa 31982, Saudi Arabia Journal Article 2026 02 09 In this study, we have put the mechanism for a Friedmann equation of modified f(G) gravity by solving it with numerical method in the view of matter with pressure-less condition. This mechanism allows us to forecast the redshift action of expansion rate of the Hubble. Here, in this paper, we have applied a Bayesian Markov Chain Monte Carlo (MCMC) technique, which is applying late time cosmic observances to put limitation on the model parameters of the Gauss Bonnet . Our understanding results in the fact that the $f(G)$ model can restore low redshift action of the standard ($\Lambda$ CDM) model. We have used Hubble (OHD), Pantheon and RSD for MCMC analysis of the logarithmic model of $f(G)$ and to constrain parameters including \(\Omega_m\) and \(H_{0}\). https://jhap.du.ac.ir/article_2098_daf649d433dbd7d7d684cd9f26c7a253.pdf