Large formula in align

This is how it looks with multline* (just to let you know):

\documentclass{article}
\usepackage{amsmath}
\begin{document}
\begin{multline*}
  \log\mathcal{L}(\alpha,\beta,\mu,\delta|  l_1,...,l_n)=\\
  \sum_{i=1}^n  \left(\log\left(\frac{\sqrt{\alpha^2-\beta^2}}{2\alpha\delta K_1 (\delta\sqrt{\alpha^2-\beta^2})} \exp\left(-\alpha\sqrt{\delta^2+(l-\mu)^2}+\beta(l-\mu)\right)\right)\right)
\end{multline*}
\end{document} 

To obtain a centred "first part" and only have two parts, I assume you just want the whole things centred. For this you just have to gather* the contents:

\documentclass{article}
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\begin{document}
\begin{gather*}
  \log \mathcal{L}(\alpha,\beta,\mu,\delta|  l_1,...,l_n) = \\
  \sum_{i=1}^n  \left( \log \left(\frac{\sqrt{\alpha^2-\beta^2}}{2\alpha \delta K_1 (\delta\sqrt{\alpha^2-\beta^2})} \exp\left(-\alpha\sqrt{\delta^2+(l-\mu)^2}+\beta(l-\mu)\right)\right) \right)
\end{gather*}
\end{document}

Note the use of \log as an operator for logarithm.

Just to comment on Karls suggestion, this is how I normally do this in order to get a more consistent look and feel. Note that the = is moved to the next line (this is generally a good idea it it may be overlooked overwise)

\documentclass{article}
\usepackage{mathtools} % autoloads amsmath
\begin{document}
\begin{align*}
  \MoveEqLeft\log\mathcal{L}(\alpha,\beta,\mu,\delta|  l_1,\dots,l_n)
 \\
  &=\sum_{i=1}^n  \left(\log\left(\frac{\sqrt{\alpha^2-\beta^2}}{2\alpha
    \delta K_1 (\delta\sqrt{\alpha^2-\beta^2})} \exp\left(-\alpha
  \sqrt{\delta^2+(l-\mu)^2}+\beta(l-\mu)\right)\right)\right)
 \end{align*}
 \end{document} 

\MoveEqLeft has a hidden & inside it, and will pull the line 2em backwards from the alignment point.