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

Lambda hypernuclei and neutron star matter in a chiral SU(3) relativistic mean field model with a logarithmic potential