code: def __lblogwealth(self, *, alpha):
      from math import log
      import scipy.optimize as so
  
      assert 0 < alpha < 1, alpha
      thres = -log(alpha)
  
      minmu = 0
      s = self.getS()
      memo = {j: self.getV(self.__get_lam_sqrttp1(j)) for j in range(2)}
  
      logwealthminmu = self.logwealthmix(
          mu=minmu, s=s, thres=thres, memo=memo
      )
      if logwealthminmu <= thres:
          return minmu
  
      maxmu = 1
      logwealthmaxmu = self.logwealthmix(
          mu=maxmu, s=s, thres=thres, memo=memo
      )
      if logwealthmaxmu >= thres:
          return maxmu
  
      res = so.root_scalar(
          f=lambda mu: self.logwealthmix(
              mu=mu, s=s, thres=thres, memo=memo
          )
          - thres,
          method="brentq",
          bracket=[minmu, maxmu],
      )
      assert res.converged, res
      return res.root
  
label_desc: Use image node_id 8 for calling the CountableDiscreteBase obj's underlying member method code with example usage: obj.__lblogwealth() and returns: res, minmu, maxmu