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Thread: Need help with Magnitude!!!

  1. #1
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    Exclamation 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!
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  2. #2
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    Quote Originally Posted by florx View Post
    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.
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