In this paper, we study the inflationary scenario in logarithmic f(R) gravity, where the rate of inflation roll is constant. On the other hand, our gravitational f(R) model is a polynomial plus a logarithmic term. We take advantage of constant-roll conditions and investigate the cosmic evolution of the logarithmic f(R) gravity. We present a numerical and a graphical study using the model parameters. Additionally, we obtain the corresponding potential by using the constant-roll condition. We obtain the exact value of the potential satisfying the constant-roll conditions. Next, we challenge it with refined swampland conjecture with respect to the Planck data. Finally, we compare our results with the latest observable data.
