I have a vector $\vec{x}$ and I want to take the logarithm of each element, forming a new vector $\vec{y} = (\log x_1, \log x_2,...,\log x_n)$. Would the following notation be understood, $\vec{y} = \log \vec{x}$ or would I have to define a logarithm operator $\hat{L} = (\log, \log, ..., \log)$ and then do $\vec{y} = \hat{L}\vec{x}$ or something like that?
I guess my question is, is there a simple way of writing the element-wise logarithm of a vector?
I would write it this way $\left(\log x_i\right)_i$, so that it is clear without further notations.