  Inflation in the framework of $f(R)$ modified gravity is revisited. We study
the conditions that $f(R)$ should satisfy in order to lead to a viable
inflationary model in the original form and in the Einstein frame. Based on
these criteria we propose a new logarithmic model as a potential candidate for
$f(R)$ theories aiming to describe inflation consistent with observations from
\textit{Planck} satellite (2015). The model predicts scalar spectral index
$0.9615<n_s<0.9693$ in agreement with observation and tensor-to-scalar ratio
$r$ of order $10^{-3}$. Furthermore, we show that for a class of models, a
natural coupling between inflation and a scalar boson is generated through the
minimal coupling between gravity and matter fields and a reheating temperature
less that $10^9$ GeV is obtained.
