# Need help with Magnitude!!!

• Mar 18th 2010, 08:52 PM
florx
Need help with Magnitude!!!
The magnitude of M of a star is a measure of its brightness B given by the formula M = -2.5 log (B/B0), where B0 is a constant, the brightness of an "average star."

a) If a star's brightness increases by a factor of 10, by how much does its magnitude increase or decrease?

I got the answer from the back of the book and it says "decreasing by -2.5." How did they get this answer? Please help me with this problem.

Thank you so much!
• Mar 18th 2010, 09:29 PM
Prove It
Quote:

Originally Posted by florx
The magnitude of M of a star is a measure of its brightness B given by the formula M = -2.5 log (B/B0), where B0 is a constant, the brightness of an "average star."

a) If a star's brightness increases by a factor of 10, by how much does its magnitude increase or decrease?

I got the answer from the back of the book and it says "decreasing by -2.5." How did they get this answer? Please help me with this problem.

Thank you so much!

I assume that your logarithm is base 10...

You are told the brightness is magnified by a factor of 10.

This means $B \to 10B$.

So $M = -2.5\log{\frac{10B}{B_0}}$

$= -2.5\left(\log{10} + \log{\frac{B}{B_0}}\right)$

$= -2.5\left(1 + \log{\frac{B}{B_0}}\right)$

$= -2.5 - 2.5\log{\frac{B}{B_0}}$.

So the magnitude has decreased by -2.5.