I checked the video and there should be a minus sign.
\begin{equation}
loss(f_{\mathbf{w},b}(\mathbf{x}^{(i)}), y^{(i)}) = \begin{cases}
- \log\left(f_{\mathbf{w},b}\left( \mathbf{x}^{(i)} \right) \right) & \text{if $y^{(i)}=1$}\\
-\log \left( 1 - f_{\mathbf{w},b}\left( \mathbf{x}^{(i)} \right) \right) & \text{if $y^{(i)}=0$}
\end{cases}
\end{equation}