tikzmath로 해봤습니다.

\documentclass{minimal}

\usepackage{tikz}

\usetikzlibrary{math}

\tikzmath{

  function mylog (\x) {

    return ln (\x) / ln (10);

  };

  real \a;

}

\def\yscale{5}

\newcommand\myloglog[1]{%

  \tikzmath{ \a=mylog(#1); }

  \node [anchor=south west,overlay,xshift=-6pt,yshift=-6pt] 

     at (#1,\a*\yscale) {\tikz\filldraw circle[radius=2pt];~{\a}};

}

\begin{document}

\begin{tikzpicture}

\draw [help lines] (0,0) grid (10,\yscale);

\foreach \x in {1,2,...,10}

  \myloglog{\x};

\end{tikzpicture}

\end{document}