The magnitude M of o star is a measure of how bright a star

The magnitude M of o star is a measure of how bright a star appears to the human eye. It is defined by M = -2.5 log(B/B_0) where B is the actual brightness of the star and B_0 is a constant. Expand the right-hand side of the equation. Use part (a) to show that the brighter a star, the less Its magnitude. Suppose B_1 and B_2 are the brightness of two stars such that B_1

Solution

(a) M = 2.5 log(B/B0)

M = 2.5 log(B) + 2.5 log(B0)

b) 2.5 log (Bo/B)

C)
M_betelgeuse = 2.5 log(B_betelgeuse) + 2.5 log(B0)
M_albiero = 2.5 log(B_albiero) + 2.5 log(B0)
with B_betelgeuse = 100* B_albiero,

so
M_betelgeuse = 2.5 log(100* B_albiero) + 2.5 log(B0)
= 2.5 log(100) -2.5 log(B_albiero) + 2.5 log(B0)
M_betelgeuse = 2.5 log(100) + M_albiero

with log(100) = 2, you get
M_betelgeuse = 2.5 * 2 + M_albiero
M_betelgeuse = 5 + M_albiero
hence Betelgeuse is 5 magnitudes less bright than Albiero