A Sobolev Space Property of Logarithm of Lipschitz functions

For a Lipschitz function $f$ on an open set in ${\mathbb{R}}^n$, we consider the $L^n$ integrability of the quotient $\frac{\mathrm{\mid }\mathrm{\nabla }f\mathrm{\mid }}{\mathrm{\mid }f\mathrm{\mid }}$ over its natural domain of definition.