  Given $n \in \{ 3,4,5 \}$ and $k > 1$ (resp. $\frac{4}{3} > k > 1$) if $n \in
\{ 3,4 \}$ (resp. $n=5$), we prove scattering of the radial $\tilde{H}^{k}:=
\dot{H}^{k}(\mathbb{R}^{n}) \cap \dot{H}^{1}(\mathbb{R}^{n})$ solutions of a
focusing size-dependent log energy-supercritical Schrodinger equation for
critical energies below that of the ground states, and for critical potential
energies below that of the ground states.
