\documentclass[a4paper]{article}

\usepackage{pgfplots}
\usepackage{pgfplots.assert}

\begin{document}

%\tracingcommands=2\tracingmacros=2


\begingroup
\makeatletter
\pgfplots@is@log@tick@a@minor@tick@pos3.0\relax
\pgfplotsassertequalstok{\pgfmathresult}{3.0}{}

\pgfplots@is@log@tick@a@minor@tick@pos3.4771213\relax
\pgfplotsassertequalstok{\pgfmathresult}{3e3}{}

\pgfplots@is@log@tick@a@minor@tick@pos1.30102999\relax
\pgfplotsassertequalstok{\pgfmathresult}{2e1}{}

\pgfplots@is@log@tick@a@minor@tick@pos-0.30102999\relax
\pgfplotsassertequalstok{\pgfmathresult}{5e-1}{}

\pgfplots@is@log@tick@a@minor@tick@pos-0.292429\relax
\pgfplotsassertequalstok{\pgfmathresult}{-0.292429}{}

\pgfplots@is@log@tick@a@minor@tick@pos3.0043\relax
\pgfplotsassertequalstok{\pgfmathresult}{3.0043}{}

\pgfplots@is@log@tick@a@minor@tick@pos-1.09691\relax
\pgfplotsassertequalstok{\pgfmathresult}{8e-2}{}
\endgroup
\end{document}

