\documentclass[a4paper]{article}
\usepackage[english]{babel}
\usepackage[utf8x]{inputenc}
\usepackage{fouriernc,amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage[colorinlistoftodos]{todonotes}
\title{Sorting Algorithm Comparison}
\author{Vivek Alumootil}
\begin{document}
\maketitle
\vspace{15mm}
\section{Merge Sort vs. Bubble Sort}
$\log_{10} n \propto n$ \\\\
$\log_{10} n \propto \log_{\sqrt[\leftroot{-3}\uproot{3}n]{n}} n$ \\\\
$\frac{\log_{\sqrt[\leftroot{-3}\uproot{3}n]{n}} n}{\log_{\sqrt[\leftroot{-3}\uproot{3}n]{n}} 10} \propto \log_{\sqrt[\leftroot{-3}\uproot{3}n]{n}} n$ \\\\
$\frac{1}{\log_{\sqrt[\leftroot{-3}\uproot{3}n]{n}} 10} \propto 1$ \\\\
$1 \propto \log_{\sqrt[\leftroot{-3}\uproot{3}n]{n}} 10$ \\\\
$\log_{\sqrt[\leftroot{-3}\uproot{3}n]{n}} n \propto 10$ \\\\
$n \propto 10^n$ \\\\
$\boxed{n \propto 10^n}$ \\\\\\\\
\end{document}
