To solve, apply the formula:
d is the distance of the star from the Earth in parsecs
m is the apparent magnitude of the star, and
M is the absolute magnitude.
Plugging-in the values of d and m to the formula, it yields an equation:
`56=10 * 10^((6.9-M)/5)`
Then, solve for M. To do so, divide both sides by 10.
Then, take the logarithm of both sides.
The right side simplifies to:
Then, multiply both sides by 5.
Subtract 6.9 from both sides.
`5log5.6 - 6.9=-M`
And, divide both sides by -1.
`-5log5.6 + 6.9=M`
Rounding off to nearest tenths, it becomes:
Therefore, the absolute magnitude of the star is 3.2 .