Can someone please prove (or point me to a proof) that the two definitions of entropy below are equivalent:

$$S=k_{B}\ln(\Omega)$$ (Statistical definition)

$$dS=\frac{\delta Q}{T}$$ for a quasistatic process (Classical definition)

Particularly i'm only interested in knowing how you would derive the classical definition from the statistical definiton, i'm not sure if it's possible the other way around nor am i interested. Thank you for your time.