# 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) )In summary, Chet is asking if the uncertainty in μ, which is calculated using the equation μ = -5 log10 (d/10), can be determined using the formula Δμ = 5 * ( Δd / d*ln(10) ). The response confirms that this method is valid as long as ln10 is in the denominator.

#### 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.

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

1 person
Yes, provided that ln10 is in the denominator.

Chet

## What is uncertainty and why is it important in scientific calculations involving logarithmic quantities?

Uncertainty is the measure of how much a measurement or calculation may vary from its true value. In scientific calculations involving logarithmic quantities, uncertainty is important because it can affect the accuracy and reliability of the results.

## How is uncertainty calculated for logarithmic quantities?

Uncertainty for logarithmic quantities is calculated using the formula: u(logx) = (ln10) x u(x) / x, where u(x) is the uncertainty in the original quantity.

## Can the uncertainty in a logarithmic quantity be negative?

No, the uncertainty in a logarithmic quantity cannot be negative. It is always a positive value representing the potential variation from the true value.

## How is uncertainty represented in scientific notation for logarithmic quantities?

Uncertainty in scientific notation for logarithmic quantities is typically written as the value of the uncertainty followed by the logarithm of the quantity, such as 2.5 x 10^-3 log(x).

## How can uncertainty be reduced in calculations involving logarithmic quantities?

Uncertainty can be reduced in calculations involving logarithmic quantities by increasing the precision and accuracy of the measurements used. Additionally, using more data points or repeating the calculation multiple times can help to reduce uncertainty.