Take the logarithm of both sides of PV^K= C. You get log(p)+ Klog(V)= log(C) which is a linear equation. Take the logarithms of P and V to get new data. Use "least squares"

http://www.ltcconline.net/greenl/cou...astSquares.htm

to get the line that best fits that data. That will be an equation of the form y= ax+ b. If you use log(V) as "x" and log(P) as "y" that will correspond to log(P)= -Klog(v)+ log(C) so K= -a and .