Comparison of exponential and logarithm function graphs with annotated axes (pgfplots). Reference figure for calculus and pre-calculus courses. From Sarmate's technical TikZ gallery (sources: MartinThoma/LaTeX-examples MIT, TeXample.net LPPL) — see also our 900+ figures on /tikz-gallery.php.
\documentclass[12pt,border=5pt]{standalone}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\usetikzlibrary{calc,angles,quotes,positioning,decorations.markings,arrows.meta,patterns,intersections,shapes,trees}
\usepackage{amsmath,amssymb}
\begin{document}
\begin{tikzpicture}
\begin{axis}[
axis x line=middle,
axis y line=middle,
grid = major,
width=16cm,
height=8cm,
grid style={dashed, gray!30},
xmin=-2.1, % start the diagram at this x-coordinate
xmax= 4.1, % end the diagram at this x-coordinate
ymin= 0, % start the diagram at this y-coordinate
ymax= 17, % end the diagram at this y-coordinate
xlabel=$x$,
ylabel=$y$,
ytick={0,2,3,4,8,9,12,16},
yticklabels={0,2,3,4,8,9,12,16},
legend cell align=left,
legend pos=south east,
legend style={draw=none},
tick align=outside,
enlargelimits=false]
% plot the function
\addplot[domain=-2:4, red, ultra thick,samples=500] {2^x};
\addplot[domain=-2:4, green!50!black, ultra thick,dashed,samples=500] {3^x};
\addplot[domain=-2:4, blue, ultra thick,dotted,samples=500] {4^x};
\legend{$2^x$,$3^x$,$4^{x}$}
\end{axis}
\end{tikzpicture}
\end{document}
