[Tex/LaTex] left alignment for equation using split

align

Goodmorning everyone,
I need your help to figure out how to align to the left an equation with a split command inside. I've alredy read all the post about it but nothing worked. Any other ideas? Thanks
Andrea

\begin{equation*}
\begin{split}
i(v)=-(\frac{520}{2000})ln(\dfrac{520}{2000})-(\frac{1480}{2000})ln(\frac{11480}{2000})=0.573,\\
p(l)=\frac{800}{2000}=0.4, \\ 
i(l)=-(\frac{320}{800})ln(\dfrac{320}{800})-(\frac{480}{800})ln(\frac{480}{800})=0.673,\\   
p(r)=\frac{1200}{2000}=0.6, \hspace{0.5cm} i(r)=-(\frac{200}{1200})ln(\dfrac{200}{1200})-(\frac{1000}{1200})ln(\frac{1000}{1200})=0.451,\\
 I=0.573-0.4(0.673)-0.6(0.451)=0.0332
    \end{split}
\end{equation*}

Best Answer

In addition to implementing David Carlisle's comments -- provide alignment points, and write \ln rather than ln -- you should also enlarge the parentheses on the right-hand side of the first five equations.

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\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{equation*}
\begin{split}
i(v)&=-\Bigl(\frac{520}{2000}\Bigr)\ln\Bigl(\dfrac{520}{2000}\Bigr)
      -\Bigl(\frac{1480}{2000}\Bigr)\ln\Bigl(\frac{11480}{2000}\Bigr)
      =0.573,\\
p(l)&= \frac{800}{2000}=0.4, \\ 
i(l)&=-\Bigl(\frac{320}{800}\Bigr)\ln\Bigl(\dfrac{320}{800}\Bigr)
      -\Bigl(\frac{480}{800}\Bigr)\ln\Bigl(\frac{480}{800}\Bigr)
      =0.673,\\   
p(r)&= \frac{1200}{2000}=0.6, \\
i(r)&=-\Bigl(\frac{200}{1200}\Bigr)\ln\Bigl(\dfrac{200}{1200}\Bigr)
      -\Bigl(\frac{1000}{1200}\Bigr)\ln\Bigl(\frac{1000}{1200}\Bigr)
      =0.451,\\[1ex]
I&=   0.573-0.4(0.673)-0.6(0.451)=0.0332
\end{split}
\end{equation*}
\end{document}
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