  An exponential modified gravity with additional logarithmic corrections is
considered with the presence of an axion-like scalar field in the role of dark
matter. Axion fields are thought to become important at late-times when the
axion-like scalar field oscillates around its vacuum expectation value,
mimicking dark matter behaviour. The model is compared with the usual
pressureless fluid description of dark matter. Both models are tested with
observational data including some of the latest sources, providing similar fits
in comparison with the $\Lambda$CDM model. Despite results are not
statistically relevant to rule out any model, the number of free parameters
still favours $\Lambda$CDM model, as shown by computing the goodness of the
fits.
