\documentclass[10pt]{article}
\usepackage{pgfplots}
\pgfplotsset{compat=1.15}
\usepackage{mathrsfs}
\usetikzlibrary{arrows}
\pagestyle{empty}
\begin{document}
\definecolor{ccqqqq}{rgb}{0.8,0.,0.}
\begin{tikzpicture}[line cap=round,line join=round,>=triangle 45,x=1.0cm,y=1.0cm]
\begin{axis}[
x=1.0cm,y=1.0cm,
axis lines=middle,
ymajorgrids=true,
xmajorgrids=true,
xmin=-4.3,
xmax=18.38,
ymin=-5.0200000000000005,
ymax=6.3,
xtick={-4.0,-3.0,...,18.0},
ytick={-5.0,-4.0,...,6.0},]
\clip(-4.3,-5.02) rectangle (18.38,6.3);
\draw[line width=
2.pt,color=ccqqqq,smooth,samples=100,domain=8.479999849328924E-8:18.38] plot(\x,{ln((\x))/ln(5.0)});
\begin{scriptsize}
\draw[color=ccqqqq] (0.26,-4.75) node {$f$};
\end{scriptsize}
\end{axis}
\end{tikzpicture}
\end{document}