More luminous?

Question

star a is seen to be ten thousand times brighter than star b. if star b has an apparent magnitude of +7.2 what is the apparent magnitude of star a?

Answer 1

5 magnitudes difference represents x 100.

10,000 = 100 x 100

so that's a difference of 5 + 5 = 10 magnitudes

so star a has an apparent magnitude of 7.2 - 10 = - 2.8

which is extremely bright for a star!