Calculating Uncertainty, involving a logarithmic quantity

[Rodger]

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.

 

[dauto]

Yes that method will give you a good estimate of the overall error.

 

[Chestermiller]

Yes, provided that ln10 is in the denominator.

Chet