The magnitude M of a star is a measure of how bright a star appears to the human eye. It is defined by
M = -2.5 log(B/B₀),
where B is the actual brightness of the star and B₀ is a constant.
(a) Expand the right-hand side of the equation.
(b) Betelgeuse is about 100 times brighter than Albiero. Use part (a) to show that Betelgeuse is 5 magnitudes less bright than Albiero. Let B1 be the brightness of the star Albiero and M1 be its magnitude.
Then 100B1 is the brightness of Betelgeuse, and its magnitude is .