  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. Therefore, we plot some figures such as the
scalar spectrum index $n_{s}$ and tensor-to-scaler ratio $r$ concerning $n$,
$\beta$ and model's constant parameters, i.e., $\alpha$, $\theta$ and $\gamma$
respectively. Also, we obtain the potential by using the constant roll
condition. We know that the potential value obtained with this condition has an
exact value. Next, we challenge it with refined swampland conjecture with
respect to the Planck data. Finally, we compare our results with the
experimental data, especially Planck 2018.
