def _compute_mag_dist_terms(cls, rup, dists, coeffs):
        """
        Compute equation (5) and implcitly equation (6):

        ``log(pre) = c + a*M + b*X - log(X + d*10^(e*M)) + epsilon``
        """

        log_pre = coeffs['c'] + coeffs['a']*rup.mag + coeffs['b']*dists.rrup \
            - np.log10(dists.rrup + coeffs['d']*10**(coeffs['e']*rup.mag))

        return log_pre
Compute equation (5) and implcitly equation (6):

        ``log(pre) = c + a*M + b*X - log(X + d*10^(e*M)) + epsilon``