logarithm-1

\documentclass[tikz,margin=8pt,convert={svg,command=\unexpanded{{inkscape\space --pdf-poppler\space --export-type="svg"\space --pages=1\space -o\space \outfile\space \infile}}}]{standalone}
\usepackage{pgfplots}
\usetikzlibrary{arrows.meta}
%
\definecolor{obsdpurple}{HTML}{8A5CF5}
%
\begin{document}
\begin{tikzpicture}[white]
	\begin{axis}[
		width=10cm,
		height=10cm,
		axis lines = center,
		enlargelimits=0.05,
		xticklabels = {\empty},
		yticklabels = {\empty},
		legend pos = north west,
		legend style = {draw=white,fill=none},
		legend image post style = -,
		legend cell align = left,
		]
	%
	\addplot [
		Latex-Latex,
		domain=-2:2, 
		samples=101, 
		color=gray,
		very thick,
		]
		{exp(x)};
	\addlegendentry{\(y=b^x\)}
	%
	\addplot [
		Latex-Latex,
		domain=0:4, 
		samples=101, 
		color=obsdpurple,
		very thick,
		]
		{ln(x)};
	\addlegendentry{\(y=\log_b(x)\)}
	%
	\addplot [
		domain=-2:4,
		samples=3,
		thick,
		dashed,
		white,
		]
		{x};
	\addlegendentry{\(y=x\)}
	%
	\end{axis}
\end{tikzpicture}
\end{document}