  We discuss the scaling of entanglement entropy in the random singlet phase
(RSP) of disordered quantum magnetic chains of general spin-S. Through an
analysis of the general structure of the RSP, we show that the entanglement
entropy scales logarithmically with the size of a block and we provide a closed
expression for this scaling. This result is applicable for arbitrary quantum
spin chains in the RSP, being dependent only on the magnitude S of the spin.
Remarkably, the logarithmic scaling holds for the disordered chain even if the
pure chain with no disorder does not exhibit conformal invariance, as is the
case for Heisenberg integer spin chains. Our conclusions are supported by
explicit evaluations of the entanglement entropy for random spin-1 and spin-3/2
chains using an asymptotically exact real-space renormalization group approach.
