The formation of a hydroxo complex is a typical example of a hydrolysis reaction. A hydrolysis reaction is one in which a substrate reacts with water, splitting a water molecule into hydroxide and hydrogen ions. In this case the hydroxide ion then forms a complex with the substrate.
In water the concentration of hydroxide is related to the concentration of hydrogen ions by the self-ionization constant, K.
The expression for hydroxide concentration is substituted into the formation constant expression
In general, for the reaction 
In the older literature the value of log K is usually cited for an hydrolysis constant. The log β value is usually cited for an hydrolysed complex with the generic chemical formula ML(OH).