  In this paper, we prove that the zero-locus of any global holomorphic
log-one-form on a projective log-smooth pair $\left(X,D\right)$ of log-general
type must be non-empty. Applying this result, we give an answer to the
algebraic hyperbolicity part of Shafarevich's conjecture, with the generic
fiber being Kawamata-log-terminal (klt) and of log-general type.
