Equation number in an array

Do wisely use {} to maintain readability.

\documentclass[preview,border=12pt]{standalone}
\usepackage{amsmath}
\begin{document}
\abovedisplayskip=0pt\relax% don't use this line in your production
\begin{equation}
\log y_i= 
\begin{cases}
    y_{2i}^* & \quad \text{if $y_{2i}^*\succ0$}\\
    0 & \quad \text{otherwise} 
\end{cases}
\end{equation}
\end{document}

load package amsmath and then replace \[ ... \] by

\begin{flalign}
...
\end{flalign}