Testing logarithmic corrections on $R^2$-exponential gravity by
  observational data
  This paper is devoted to the analysis of a class of $F(R)$ gravity, where
additional logarithmic corrections are assumed. The gravitational action
includes an exponential term and a $R^2$ inflationary term, both with
logarithmic corrections. This model can unify an early time inflationary era
and also the late time acceleration of the universe expansion. This model is
deeply analysed, confronting with recent observational data coming from the
largest Pantheon Type Ia supernovae sample, the latest measurements of the
Hubble parameter $H(z)$, manifestations of Baryon Acoustic Oscillations and
Cosmic Microwave Background radiation. The viability of the model is studied
and the corresponding constraints on the free parameters are obtained, leading
to an statistical analysis in comparison to $\Lambda$CDM model. The
inflationary era is also analysed within this model and its compatibility with
the latest observational data for the spectral index of primordial curvature
perturbations and the scalar-to-tensor ratio. Finally, possible corrections on
the Newton's law and constraints due to primordial nucleosynthesis are
analysed.
