Two stars have magnitudes of 4 and 9 respectively. How much brighter is the star

Question

Two stars have magnitudes of 4 and 9 respectively. How much brighter is the star with magnitude 4 than the star with magnitude 9? If these two star were the same absolute magnitude (-4), how much further is the star with apparent magnitude of 9 than the star with the apparent magnitude of 4?

Please show work with answers for the following:   

Brightness of the 4th magnitude versus 9th magnitude:

Distance of magnitude 4:      

Distance of magnitude 9:

Ratio of distance of magnitude 9/magnitude 4:

Explanation / Answer

mass =4
mass =9
f/f = 10^[0.4(mm)] = 100
We have studied in the inverse square law that if two stars have intrinsically the same luminosity, but one of them appears 100 times brighter than the other, the ratio is 10 but it doesnot tells us which one is farther and which one is nearer
Mass = 4
Mass = 4
d = 10^[0.2(mM)+1] = 398.107 pc
d = 10^[0.2(mM)+1] = 3981.07 pc
second star is 10 times farther away than first star

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