\documentclass[10pt,a4paper]{article}

% Packages
\usepackage{fancyhdr}           % For header and footer
\usepackage{multicol}           % Allows multicols in tables
\usepackage{tabularx}           % Intelligent column widths
\usepackage{tabulary}           % Used in header and footer
\usepackage{hhline}             % Border under tables
\usepackage{graphicx}           % For images
\usepackage{xcolor}             % For hex colours
%\usepackage[utf8x]{inputenc}    % For unicode character support
\usepackage[T1]{fontenc}        % Without this we get weird character replacements
\usepackage{colortbl}           % For coloured tables
\usepackage{setspace}           % For line height
\usepackage{lastpage}           % Needed for total page number
\usepackage{seqsplit}           % Splits long words.
%\usepackage{opensans}          % Can't make this work so far. Shame. Would be lovely.
\usepackage[normalem]{ulem}     % For underlining links
% Most of the following are not required for the majority
% of cheat sheets but are needed for some symbol support.
\usepackage{amsmath}            % Symbols
\usepackage{MnSymbol}           % Symbols
\usepackage{wasysym}            % Symbols
%\usepackage[english,german,french,spanish,italian]{babel}              % Languages

% Document Info
\author{Snith}
\pdfinfo{
  /Title (expo-and-log.pdf)
  /Creator (Cheatography)
  /Author (Snith)
  /Subject (Expo and Log Cheat Sheet)
}

% Lengths and widths
\addtolength{\textwidth}{6cm}
\addtolength{\textheight}{-1cm}
\addtolength{\hoffset}{-3cm}
\addtolength{\voffset}{-2cm}
\setlength{\tabcolsep}{0.2cm} % Space between columns
\setlength{\headsep}{-12pt} % Reduce space between header and content
\setlength{\headheight}{85pt} % If less, LaTeX automatically increases it
\renewcommand{\footrulewidth}{0pt} % Remove footer line
\renewcommand{\headrulewidth}{0pt} % Remove header line
\renewcommand{\seqinsert}{\ifmmode\allowbreak\else\-\fi} % Hyphens in seqsplit
% This two commands together give roughly
% the right line height in the tables
\renewcommand{\arraystretch}{1.3}
\onehalfspacing

% Commands
\newcommand{\SetRowColor}[1]{\noalign{\gdef\RowColorName{#1}}\rowcolor{\RowColorName}} % Shortcut for row colour
\newcommand{\mymulticolumn}[3]{\multicolumn{#1}{>{\columncolor{\RowColorName}}#2}{#3}} % For coloured multi-cols
\newcolumntype{x}[1]{>{\raggedright}p{#1}} % New column types for ragged-right paragraph columns
\newcommand{\tn}{\tabularnewline} % Required as custom column type in use

% Font and Colours
\definecolor{HeadBackground}{HTML}{333333}
\definecolor{FootBackground}{HTML}{666666}
\definecolor{TextColor}{HTML}{333333}
\definecolor{DarkBackground}{HTML}{7DC6F0}
\definecolor{LightBackground}{HTML}{EEF7FD}
\renewcommand{\familydefault}{\sfdefault}
\color{TextColor}

% Header and Footer
\pagestyle{fancy}
\fancyhead{} % Set header to blank
\fancyfoot{} % Set footer to blank
\fancyhead[L]{
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{C}
    \SetRowColor{DarkBackground}
    \vspace{-7pt}
    {\parbox{\dimexpr\textwidth-2\fboxsep\relax}{\noindent
        \hspace*{-6pt}\includegraphics[width=5.8cm]{/web/www.cheatography.com/public/images/cheatography_logo.pdf}}
    }
\end{tabulary}
\columnbreak
\begin{tabulary}{11cm}{L}
    \vspace{-2pt}\large{\bf{\textcolor{DarkBackground}{\textrm{Expo and Log Cheat Sheet}}}} \\
    \normalsize{by \textcolor{DarkBackground}{Snith} via \textcolor{DarkBackground}{\uline{cheatography.com/185705/cs/38840/}}}
\end{tabulary}
\end{multicols}}

\fancyfoot[L]{ \footnotesize
\noindent
\begin{multicols}{3}
\begin{tabulary}{5.8cm}{LL}
  \SetRowColor{FootBackground}
  \mymulticolumn{2}{p{5.377cm}}{\bf\textcolor{white}{Cheatographer}}  \\
  \vspace{-2pt}Snith \\
  \uline{cheatography.com/snith} \\
  \end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Cheat Sheet}}  \\
   \vspace{-2pt}Not Yet Published.\\
   Updated 21st May, 2023.\\
   Page {\thepage} of \pageref{LastPage}.
\end{tabulary}
\vfill
\columnbreak
\begin{tabulary}{5.8cm}{L}
  \SetRowColor{FootBackground}
  \mymulticolumn{1}{p{5.377cm}}{\bf\textcolor{white}{Sponsor}}  \\
  \SetRowColor{white}
  \vspace{-5pt}
  %\includegraphics[width=48px,height=48px]{dave.jpeg}
  Measure your website readability!\\
  www.readability-score.com
\end{tabulary}
\end{multicols}}




\begin{document}
\raggedright
\raggedcolumns

% Set font size to small. Switch to any value
% from this page to resize cheat sheet text:
% www.emerson.emory.edu/services/latex/latex_169.html
\footnotesize % Small font.

\begin{multicols*}{3}

\begin{tabularx}{5.377cm}{x{2.05965 cm} p{0.50347 cm} x{2.01388 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{Laws of exponents}}  \tn
% Row 0
\SetRowColor{LightBackground}
a\textasciicircum{}m\textasciicircum{} × a\textasciicircum{}n\textasciicircum{} & = & a\textasciicircum{}m + n\textasciicircum{} \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
a\textasciicircum{}m\textasciicircum{} ÷ a\textasciicircum{}n\textasciicircum{} & = & a\textasciicircum{}m - n\textasciicircum{} \tn 
% Row Count 2 (+ 1)
% Row 2
\SetRowColor{LightBackground}
(a\textasciicircum{}m\textasciicircum{})\textasciicircum{}n\textasciicircum{} & = & a\textasciicircum{}mn\textasciicircum{} \tn 
% Row Count 3 (+ 1)
% Row 3
\SetRowColor{white}
(a / b)\textasciicircum{}m\textasciicircum{} & = & a\textasciicircum{}m\textasciicircum{} / b\textasciicircum{}m\textasciicircum{} \tn 
% Row Count 4 (+ 1)
% Row 4
\SetRowColor{LightBackground}
(a ± b)\textasciicircum{}m\textasciicircum{} & ≠ & a\textasciicircum{}m\textasciicircum{} ± b\textasciicircum{}m\textasciicircum{} \tn 
% Row Count 5 (+ 1)
% Row 5
\SetRowColor{white}
a\textasciicircum{}-m\textasciicircum{} & = & 1 / a\textasciicircum{}m\textasciicircum{} \tn 
% Row Count 6 (+ 1)
% Row 6
\SetRowColor{LightBackground}
a\textasciicircum{}m / n\textasciicircum{} & = & \textasciicircum{}n\textasciicircum{}√a\textasciicircum{}m\textasciicircum{} \tn 
% Row Count 7 (+ 1)
% Row 7
\SetRowColor{white}
1\textasciicircum{}a\textasciicircum{} & = & 1 \tn 
% Row Count 8 (+ 1)
% Row 8
\SetRowColor{LightBackground}
a\textasciicircum{}0\textasciicircum{} & = & 1 \tn 
% Row Count 9 (+ 1)
% Row 9
\SetRowColor{white}
0\textasciicircum{}a\textasciicircum{} & = & 0 \tn 
% Row Count 10 (+ 1)
% Row 10
\SetRowColor{LightBackground}
0\textasciicircum{}0\textasciicircum{} & → & not defined \tn 
% Row Count 11 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.33427 cm} p{0.4577 cm} x{1.78503 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{Radicals}}  \tn
% Row 0
\SetRowColor{LightBackground}
even root of positive number & → & postive and negative \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
even root of negative number & → & none \tn 
% Row Count 4 (+ 2)
% Row 2
\SetRowColor{LightBackground}
odd root of positive number & → & positive \tn 
% Row Count 6 (+ 2)
% Row 3
\SetRowColor{white}
odd root of negative number & → & negative \tn 
% Row Count 8 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.19696 cm} p{0.4577 cm} x{1.92234 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{Operations}}  \tn
% Row 0
\SetRowColor{LightBackground}
a \textasciicircum{}n\textasciicircum{}√c ± b \textasciicircum{}n\textasciicircum{}√c & = & (a ± b) \textasciicircum{}n\textasciicircum{}√c \tn 
% Row Count 2 (+ 2)
% Row 1
\SetRowColor{white}
a \textasciicircum{}n\textasciicircum{}√c × b \textasciicircum{}n\textasciicircum{}√d & = & (a × b) \textasciicircum{}n\textasciicircum{}√(c × d) \tn 
% Row Count 4 (+ 2)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.01388 cm} p{0.4577 cm} x{2.10542 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{Conjugate}}  \tn
% Row 0
\SetRowColor{LightBackground}
\textasciicircum{}n\textasciicircum{}√a + \textasciicircum{}n\textasciicircum{}√b & → & \textasciicircum{}n\textasciicircum{}√a - \textasciicircum{}n\textasciicircum{}√b \tn 
% Row Count 1 (+ 1)
% Row 1
\SetRowColor{white}
\textasciicircum{}n\textasciicircum{}√a - \textasciicircum{}n\textasciicircum{}√b & → & \textasciicircum{}n\textasciicircum{}√a + \textasciicircum{}n\textasciicircum{}√b \tn 
% Row Count 2 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{x{2.70043 cm} p{0.4577 cm} x{1.41887 cm} }
\SetRowColor{DarkBackground}
\mymulticolumn{3}{x{5.377cm}}{\bf\textcolor{white}{Finding the root of x ± 2√y}}  \tn
% Row 0
\SetRowColor{LightBackground}
√((a + b) + 2√(ab)) & = & √a + √b \tn 
% Row Count 1 (+ 1)
\hhline{>{\arrayrulecolor{DarkBackground}}---}
\end{tabularx}
\par\addvspace{1.3em}

\begin{tabularx}{5.377cm}{X}
\SetRowColor{DarkBackground}
\mymulticolumn{1}{x{5.377cm}}{\bf\textcolor{white}{Properties of logarithms}}  \tn
\SetRowColor{white}
\mymulticolumn{1}{x{5.377cm}}{} \tn 
\hhline{>{\arrayrulecolor{DarkBackground}}-}
\end{tabularx}
\par\addvspace{1.3em}


% That's all folks
\end{multicols*}

\end{document}