The log10(M) function computes the element-wise base-10 logarithm of M.  The result, R, is formed as R[i,j] = log10(M[i,j]).

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

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

$\mathrm{log10}\left(M\right)$

$\left[\begin{array}{cc}\mathrm{-0.5228787453}& \mathrm{-0.6989700043}\\ \mathrm{-1.000000000}& \mathrm{-0.3979400087}\end{array}\right]$