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how to make maths equations start at the left?

$$ \lim_{ x \to 0} \frac{\log {10 + \log(x+ \frac{1}{10})}}{x} = 10 $$

this display on center we want to start it left

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4  
Don't use $$ ... $$ for display math; you should read this. –  Jubobs Mar 27 at 0:37
    
Welcome to TeX.SX! –  Adam Liter Mar 27 at 0:50
    
@Jubobs -- not the same. the cited question asks for left alignment within a list environment. –  barbara beeton Mar 27 at 0:53
    
@barbarabeeton You're right: wrong question. I'll retract my close vote. However, I'm confident this question has a duplicate somewhere on the site... –  Jubobs Mar 27 at 1:39

2 Answers 2

\documentclass{article}
\usepackage{amsmath}
\usepackage{showframe}   %% just for demo
\begin{document}
  \begin{flalign}
     \lim_{ x \to 0} \frac{\log {10 + \log(x+ \frac{1}{10})}}{x} = 10 && 
  \end{flalign}
\end{document}

enter image description here

If you want all your equations to start from left, add [fleqn] option to the \documentclass. Further, you may want to set \mathindent to zero.

\documentclass[fleqn]{article}
\usepackage{amsmath}
\usepackage{showframe}   %% just for demo
\setlength\mathindent{0pt}
\begin{document}
  \[
    \lim_{ x \to 0} \frac{\log {10 + \log(x+ \frac{1}{10})}}{x} = 10 
  \]
\end{document}

enter image description here

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Another method that works with all display math environments, if you don't want all equation to be aligned on the left margin, is the following.

We define a new command

\newcommand{\mathleft}{\@fleqntrue\@mathmargin0pt}

that simulates the option fleqn with \mathindent=0pt, and a new command to restore the normal behavior

\newcommand{\mathcenter}{\@fleqnfalse}

In the following MWE you can see how to use those commands:

\documentclass{article}
\usepackage{showframe} % just for the example
\usepackage{amsmath}

\makeatletter
\newcommand{\mathleft}{\@fleqntrue\@mathmargin0pt}
\newcommand{\mathcenter}{\@fleqnfalse}
\makeatother

\begin{document}

\mathleft
\begin{equation}
\lim_{ x \to 0} \frac{\log {10 + \log(x+ \frac{1}{10})}}{x} = 10
\end{equation}
\mathcenter

\begin{equation}
\lim_{ x \to 0} \frac{\log {10 + \log(x+ \frac{1}{10})}}{x} = 10
\end{equation}

\end{document} 

Output

enter image description here

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