The Intuitive Logarithm

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.