We propose [Sobouti, arXiv:astro-ph/0603302] an f(R) modification of GR, which admits of a modified Schwarzschild metric. In the weak field limit this amounts to adding a small logarithmic correction to the newtonian potential. A test star moving in such a spacetime acquires a constant speed at large distances. From observations of the velocity curves of spirals, this speed turns out to be proportional to the fourth root of the mass of the central body, in compliance with the Tully-Fisher relation. A variance of MOND emerges as a consequence of the formalism.