In this study, we begin by deriving a two-term strong converse inequality that characterizes the rate of approximation for generalized exponential sampling operators, utilizing the logarithmic moduli of smoothness. Subsequently, we combine the direct and converse estimates to establish the saturation property and identify the class of these approximation operators. Finally, we provide the results for the generalized exponential sampling series using specific kernels that meet the necessary assumptions. It should be noted that in the present study we follow a direct approach within the framework of Mellin analysis in the processes obtained.