Big-O Notation's Pgfplots Representation - latex

Question

I am looking for graphs of big-o notation terms below;
O(1) is a constant time complexity
O(n) is a linear time complexity
O(log_2(n)) is a logarithmic time complexity (I mean log basis 2)
O(n log_2(n))
O(n^2) is a quadratic time complexity
O(n^3) cubic time complexity
O(2^n) exponential time complexity
Could you help me to represent these big O notations using pgfplots?
I have tried this code snipped for log_2(n). To tell the truth, I'm not so sure.
\documentclass[border=50pt]{standalone}
\usepackage{pgfplots}
\begin{document}
\begin{tikzpicture}[trim axis left]
\begin{axis}
[
axis lines = left,
xlabel = \(n\),
ylabel = {\(\log_{2}(n)\)},
]
[domain=0:10,
samples=1000,
enlarge x limits=false,
grid=both,
no markers,
axis equal,
legend pos=outer north east,
legend style={draw=none},]
\addplot +[thick] {ln(x)/ln(2)};
\addlegendentry{$\log_{2}(n)$};
\end{axis}
\end{tikzpicture}
\end{document}

Answer 1

You were almost there ... The only missing parts were other functions and proper axes configuration. Here is my solution. You might need to think about the ranges. I am not entirely sure they are correct but did not bother to check. I changed a way you to make the graph itself centred; I think overlay works better.
\documentclass[margin=50pt]{standalone}
\usepackage{pgfplots}
\pgfplotsset{width=12cm,compat=1.18}
\begin{document}
\begin{tikzpicture}
\begin{axis}
[
axis lines = left,
xmin=1, xmax=8.1, ymin=1, ymax=9,
domain=0:8, samples=100, no markers, thick, grid=both,
xlabel = \(n\), ylabel = {\(f(n)\)},
label style = {overlay}, % Has he same effect as
ticklabel style = {overlay}, % trim axis [left|right]
legend entries = {
$1$,
$\log_{5}n$,
$\log_{2}n$,
$n$,
$n\log_{2}n$,
$2^{n}$,
$n^{2}$,
$n^{3}$,
},
every axis/.style = {font=\footnotesize},
label style = {font=\normalsize},
]
\addplot+ {1};
\addplot+ {1 + ln(x)/ln(5)};
\addplot+ {1 + ln(x)/ln(2)};
\addplot+ {x};
\addplot+ {1 + x*ln(x)/ln(2)};
\addplot+ {2^x-1};
\addplot+ {x^2};
\addplot+ {x^3};
\end{axis}
\end{tikzpicture}
\end{document}