\documentclass{standalone}
\standaloneconfig{border=2mm 2mm 2mm 2mm}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}

\begin{document}
  \begin{tikzpicture}[scale=0.50]
      \begin{axis}[axis lines=center,
    xlabel={$x$},
    ylabel={$y$},
    xtick=\empty,ytick=\empty,
    xmin=0,xmax=7,
    ymin=0,ymax=10,
    unbounded coords=jump,
    samples=200]
    \addplot [red,thick,domain=1.3:7,unbounded coords=jump]
    {x-1+1/(ln(x))};
    \addplot [blue,thick,domain=1:7,unbounded coords=jump]
    {x*1.048-1};
    \node[rotate=35,below] at (6,5) {$y=ax+b$};
       \end{axis}
  \end{tikzpicture}
\end{document}