The connection between the number of microstates,W, and the entropy, S, of a system is expressed by the Boltzmann equation
S=k*ln*W

where k is the Boltzmann constant per molecule (particle)1.38*10^-23, . From this equation the entropy change,delta S , for a system can be related to the change in the number of microstates as
delta S=k*ln(W final/W initial)

where w final in the final number of microstates and w initial is the initial number of microstates.

A gaseous system undergoes a change in temperature and volume. What is the entropy change for a particle in this system if the final number of microstates is 0.458 times that of the initial number of microstates?
Express your answer numerically in joules per kelvin per particle.