As mass increases from            0.08    M(solar)   to         90 M(solar)

luminosity increases from approx      0.0005  L(solar)       1,000,000 L(solar)


           Q:  If luminosity depends on mass to some power,


                     L  =  K M^q


               what is the approximate value of the exponent q?




      To find the answer, take the log base 10 of both sides:

 
                   log(L)  =  log(K) + q*log(M)


      Then solve for q using data for several stars:


                                 change in log(L)
                           q  =  ----------------
                                 change in log(M)


      Choosing M = 0.08 and M = 90, 

                                 log(1,000,000) - log(0.0005)
                           q  =  -----------------------------
                                      log(90) - log(0.08)


                                    9.3
                              =   --------------
                                    3.05


                              =    3.0