Problem 8.42 asks for some math that you may not remember because we didn't review it in Phy 131.  In part c, the question is, if a fraction f of the energy remains after one collision, how many collisions N are required in order to reduce the energy by a fraction F?  Here F is given to be 1/59,000.  The idea is that after two collisions, the energy has become a fraction f² of the original energy.  After N collisions, the energy has become a fraction f^N of the original, and this should be equal to F.  Taking logarithms of both sides of this equality, we find that N=log(F)/log(f).  This piece of math is true whether the logarithm is in base 10, or base e, or any other base.