How Can an Astronomer Derive the Distance to Alpha Centauri B?

[Physics Dad]

Homework Statement

An astronomer has independent measurements of both the apparent and absolute magnitudes of Alpha Centauri B, and a measurement of the extinction towards the star. Derive an algebraic expression for the distance to the star and a second expression that shows how the uncertainty associated with this distance can be estimated.

Homework Equations

(m-A_v)-M=5log(d)-5

The Attempt at a Solution

OK, so I know that the above is the equation which contains all of the parameters I need and I know I can rearrange this equation to give me d, but that isn't deriving it.

Do I have to do a lot more than this?

Also, if this is correct then I know that I will end up with an equation that looks like this:

d=10^{1/5(m-M-A_v+5)}

And I know that uncertainties is simply adding in quadrature, but I get very confused here as I have many variables all as a power of another number and I don't know how to approach this.

I don't want answers, I just want guidance.

Many thanks

 

[mfb]

Gaussian error propagation. If y=f(x), then $\Delta y = \left| \frac{\rm{d}f}{\rm{dx}} \right| \Delta x$ if $\Delta x$ is small enough. Add multiple sources in quadrature, if necessary.