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Homework Help: Calculating Uncertainty, involving a logarithmic quantity

  1. May 17, 2014 #1
    Essentially I'm asking if the uncertainty in μ = -5 log10 (d/10) is given by Δμ = 5 * ( Δd / d*ln(10) )

    1. The problem, all variables and given/known data

    I am to calculate the uncertainty in absolute magnitude (M), which is calculated using an equation involving logs.

    The equation for M is: M = m - 5 log10 (d/10) where m and d have associated errors Δm and Δd.

    3. The attempt at a solution

    I introduce: μ = -5 log10 (d/10) such that M = m + μ

    Then I calculate the error in μ whereby: Δμ = 5 * ( Δd / d*ln(10) )

    I then calculate the error in M by:

    ΔM2 = [ Δm2 + Δμ2 ]

    Any comments on this would be greatly appreciated as I have 0 confidence in myself when it comes to calculating errors.
  2. jcsd
  3. May 17, 2014 #2
    Yes that method will give you a good estimate of the overall error.
  4. May 17, 2014 #3
    Yes, provided that ln10 is in the denominator.

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