Distance Modulus - Formula and Problems

Distance Modulus!
m - M = 5 * log(d) - 5
m = apparent magnitude
M = absolute magnitude
d = distance (pc)

Practice Problems Included:
Type 1a Supernovae are caused when a white dwarf begins to accrete matter from a companion star. Once the white dwarf reaches 1.4 solar masses, it goes supernova. Because of how consistent they are, Type 1a supernovae are very helpful in measuring distance to far-away galaxies. They have an absolute magnitude of -19.3. If a Type tIa supernova was observed to have an apparent magnitude of 10.4, how far is it in parsecs?

A star has an apparent magnitude of -5 and has an absolute magnitude of -26.3. How far away is the star? Give your answer in Mpc.

If a star's distance modulus is zero, how far away would the star be?

The absolute magnitude of a star is -26. Find the apparent magnitude of the star if it was 30 pc away.