The solution to \(z = {\text{log}}\left( {e^{x} e^{y} } \right)\) is \(x + y\) in some commutative algebra \(A\) . However, when \(A\) is not commutative, \(z \ne x + y\) . In general, \(z\) can be expressed as \(x + y\) plus a sum of formal power series of \(x\) and \(y\) in commutators, that is called Campbell-Baker-Hausdorff (CBH) formula, or the Hausdorff series. Some of its terms are given as follows. \(z = z_{1} + z_{2} + \cdots\) where \(z_{1} = x + y\) , \(z_{2} = \frac{1}{2} \left[ {x,y} \right]\) , \(z_{3} = \frac{1}{12} \left[ {x,\left[ {x,y} \right]} \right] + \frac{1}{12} \left[ {y,\left[ {y,x} \right]} \right], \ldots\) In this study, we survey the Hausdorff series evaluated in different monoid rings.