The log(M) function computes the element-wise natural logarithm of M.  The result, R, is formed as R[i,j] = log(M[i,j]).

$\mathrm{with}\left(\mathrm{MTM}\right)\:$

$M≔\mathrm{Matrix}\left(\left[\left[0.3\,0.2\right]\,\left[0.1\,0.4\right]\right]\right)\:$

$\log \left(M\right)$

$\left[\begin{array}{cc}\mathrm{-1.203972804}& \mathrm{-1.609437912}\\ \mathrm{-2.302585093}& \mathrm{-0.9162907319}\end{array}\right]$