I am going through this course. The professor is talking about the logistic regression cost function:
$$ P(y|x) = \hat y^y (1- \hat y)^{(1-y)} $$
Taking log on both sides provides:
$$ \begin{align} log[P(y|x)] &= log[\hat y^y (1- \hat y)^{(1-y)}]\\ &= - L(\hat y,y) \end{align} $$
Why does the logistic regression cost function need to be the negative of log?