% !TeX TXS-program:compile = txs:///pdflatex

\documentclass[margin=5mm]{standalone}
\usepackage[nonpgfplots]{tkz-grapheur}

\begin{document}

\begin{GraphiqueTikz}[x=5cm,y=5cm,Xmin=-0.3,Xmax=1.075,Xgrille=0.2,Xgrilles=0.2,Ymin=0,Ymax=1.075,Ygrille=0.2,Ygrilles=0.2]
	\TracerAxesGrilles[Police=\footnotesize]{-0.2,0,0.2,0.4,0.6,0.8,1}{0.2,0.4,0.6,0.8,1}
	\DefinirCourbe[Trace,Nom=cg,Couleur=teal]{log(x+2)}
	\DefinirPts{A/0.3125/0,M/0.3125/{ln(0.3125+2)},J/0/1}
	\draw[teal] (-0.2,0.45) node[font=\large,left] {$\mathcal{C}_{g}$} ;
	\MarquerPts{(A)/$\vphantom{M}x$/below,(M)/$M$/below right,(J)/$J$/above right}
	\draw[pfltraitantec] (A)--(M);
	\draw[pflpoint] (M)--(J);
\end{GraphiqueTikz}

\end{document}