Calculating Uncertainty, involving a logarithmic quantity

  • Thread starter Rodger
  • Start date
  • #1
Rodger
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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.


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.
 

Answers and Replies

  • #2
dauto
1,948
201
Yes that method will give you a good estimate of the overall error.
 
  • #3
22,331
5,205
Yes, provided that ln10 is in the denominator.

Chet
 

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