  We introduce the intuitive method to select an analytic Abel function of an
analytic function f at a non-fixpoint. Due to the complexity of this method by
involving matrix inversion of increasing size there is little known about its
convergence.
  We show its convergence in the simplest but still complicated case f(x)=bx.
We show that the obtained Abel function is, as expected, the logarithm to base
b, independent on its development point. As a by-product we obtain a new
polynomial approximation sequence for the logarithm to base b.
