  In this article we present new gradient estimates for positive solutions to a
class of nonlinear elliptic equations involving the f-Laplacian on a smooth
metric measure space. The gradient estimates of interest are of Souplet-Zhang
and Hamilton types respectively and are established under natural lower bounds
on the generalised Bakry-\'Emery Ricci curvature tensor. From these estimates
we derive amongst other things Harnack inequalities and general global
constancy and Liouville-type theorems. The results and approach undertaken here
provide a unified treatment and extend and improve various existing results in
the literature. Some implications and applications are presented and discussed.
