Dimensional equation for measuring logarithm of volume

I have a measure that uses radiation dose (M.U. $Gray$) and $\log(Volume)$. The measure is $[\frac{Dose}{\log(Volume)}]$ that is $[\frac{D}{\log(l^3)}]$ with $D$ as radiation dose (M.U. unit is Gray ) and $l$ is length (M.U. in international measure units is meter ). What is the correct measure unit for this kind of measure after the following steps $[\frac{D}{\log(l^3)}]\Leftrightarrow [\frac{D}{3\log(l)}]\Rightarrow [\frac{D}{\log(l)}]$ that is, what is the transformation of logarithm of length $\log(l)$?