  We study spherically symmetric static empty space solutions in
$R+\varepsilon/R$ model of $f(R)$ gravity. We show that the Schwarzschild
metric is an exact solution of the resulted field equations and consequently
there are general solutions which {are perturbed Schwarzschild metric and
viable for solar system. Our results for large scale contains a logarithmic
term with a coefficient producing a repulsive gravity force which is in
agreement with the positive acceleration of the universe.
