At a water treatment plant, using a particle counter, it was determined that the source $($raw$)$ water contains $20,952$ particles $\frac{?}{mL}.$

a$)$ Calculate the log removal associated with each of the following inactivation levels: $68\%,96\mathrm{.}8\%$ and $99\mathrm{.}7\%$

b$)$ If the treatment process achieves $3-$log removal, compute the number of particles in the treated water.