Answer
a. $M = -2.5 (\log B - \log B_{0})$
b. See explanation below
c. See explanation below
Work Step by Step
a. Expand $M = -2.5 \log (\frac{B}{B_{0}})$
$M = -2.5 (\log B - \log B_{0})$
b. Show that the bighter a star, the less its magnitude
Let's say that B is 10, then 100 and assume that $B_{0} = 1$
$M = -2.5 (\log (10) - \log (1))$
$M = -2.5 (1 - 0)$
$M = -2.5$
$M = -2.5 (\log (100) - \log (1))$
$M = -2.5 (2 - 0)$
$M = -5.0$
Thus it is less of a magnitude
c. Show that Betelgeus is 5 magnitudes less bright than Albiero
log 100 = 2
2 * 2.5 = 5
Thus, it is 5 magnitudes less bright than Aliero
