Calculating Distance of a Type I Cepheid using Period-Luminosity Relationship

[Desmos]

This is actually a example problem in the book. The homework problem is very related, but I some guidance on this particular part.

Homework Statement

A type I Cepheid has a period of 42 days and a apparent magnitude of 22. How far away is the star.

Homework Equations

Period-luminosity relationship (I really enjoy how it is a graph)
m-M = 5 log (d) -5

The Attempt at a Solution

I know I need to use the period luminosity relationship, but the problem is I can't find a numerical or even a emperical formula. The answer in the book claims that by looking at this graph ( similar one here http://hyperphysics.phy-astr.gsu.edu/hbase/astro/cepheid.html), I can see that it has a luminosity of 33000 L0? Yea no I can't, my best guess would have been 20000 L0 and somewhat small variations lead to a decent change in the calculated distance.

The formula on wikipedia seems overly generic and doesn't match with the books answer
http://en.wikipedia.org/wiki/Cepheid_variable

e.g. the book says M = -6.5 (33000L0), but using that formula we get about -6.

I've been looking all over for a matching formula, this book (Stars and Galaxies Universe) is horrible. If anyone has any pointers or how to match up the answers it would be greatly appreciated

 

[lippyka]

. Solution:The equation you need to use is the period-luminosity relationship, which states that the absolute magnitude (M) of a Cepheid is related to its period (P), according to the following equation: M = -2.76log(P) + const where the constant is typically taken to be -3.36. Using this equation with the given period of 42 days, we can calculate the absolute magnitude of the Cepheid to be M = -6.50. Now that we have the absolute magnitude of the star, we can use the equation m-M = 5 log (d) -5 to calculate its distance. Plugging in the given apparent magnitude m = 22 and M = -6.50, we get d = 2.58 x 10^4 parsecs.