Question

The difference between the a parent magnitude (brightness) m of a star, and its absolute magnitude M is given by the formula m - M = 5log d/10, where d is the distance of the star from Earth, measured in parsecs.

a. Find the distance d of Antares from Earth.
b. Sigma Sco is 225 parsecs from Earth. Find its absolute magnitude.
c. How many times as great is the distance to Antares as the distance to Rho Oph?

Extra information:
Rho Oph (m = 5.0, M = -0.4)
Sigma Sco (m = 2.9)
Antares (m = 1.0, M = 5.3)