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 separ
ation energies of single- and double-$Lambda$ hypernuclei are well explained. The nuclear matter equation of state (EOS) is found to be softened by $sigmazeta$ mixing which comes from determinant interaction. The neutron star matter EOS is further softened by $Lambda$ hyperons.
