  We develop a chiral SU(3) symmetric relativistic mean field (RMF) model with
a logarithmic potential of scalar condensates. Experimental and empirical data
of symmetric nuclear matter saturation properties, bulk properties of normal
nuclei, and separation energies of single- and double-$\Lambda$ hypernuclei are
well explained. The nuclear matter equation of state (EOS) is found to be
softened by $\sigma\zeta$ mixing which comes from determinant interaction. The
neutron star matter EOS is further softened by $\Lambda$ hyperons.
