Reaction rate and the equilibrium rate

the equilibrium rate involves the constant, K, such as the eq constant = [products]/[reactants]
How does that k relate to Gibbs free energy? Do you simply plug it into the equation -RTlnK? I'm just very confused because my Ochem book says -RTlnK= -2.303RTlogK and I'm not sure where they got this constant -2.303...

Also, does the above k relate at all to the rate constant k where the rate of a reaction = k[product1][product2] .... Or is k just a standard variable to denote constants..

Thanks...

Reaction rate and the equilibrium rate