If i have a=exp x, and i know that my uncertainty in a is 3% ( at all

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In summary, the conversation discusses how to calculate the uncertainty in x when given the uncertainty in a and a specific value for a. The suggested method is to use error propagation and the formula for x=ln(a). However, there is an issue with the resulting units and it is clarified that the absolute uncertainty in x is equal to the percentage uncertainty in a.
  • #1
lavster
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if i have a=exp x, and i know that my uncertainty in a is 3% ( at all points). At a point where a=2, how do we calculate the uncdrtainty in x.

is the absolute value = (3% of ln 2)/ln 2, which equals 0.03mm, which equals 1% (if x is 3mm)

thanks
 
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  • #2
x cannot have units of mm in that equation, and a=2 does not correspond to x=3.

Use error propagation - write the expression as x=ln(a), the derivative with respect to a is easy to find then.
The formula looks good, but the result has the problem mentioned above.
 
  • #3
so dx = da/a?

so the absolute uncertainty in x is equal to the percentage uncetainty in a?
 
  • #5


I would like to clarify that the uncertainty in a is not necessarily constant at all points. It may vary depending on the experimental conditions and the precision of the measurements. However, assuming that the uncertainty in a is 3% at all points, we can use the formula for error propagation to calculate the uncertainty in x.

First, we need to express a=exp(x) in terms of x, which gives us x=ln(a). Then, using the formula for error propagation, the uncertainty in x can be calculated as:

δx = (∂x/∂a) * δa

where δx is the uncertainty in x, δa is the uncertainty in a, and (∂x/∂a) is the partial derivative of x with respect to a.

In this case, (∂x/∂a) = 1/a, which gives us:

δx = (1/a) * δa

Substituting the values, we get:

δx = (1/2) * (0.03) = 0.015

Therefore, the uncertainty in x is 0.015 or 1.5% when a=2. This means that the absolute value of the uncertainty in x is 0.03mm, which is 1% of the value of x (3mm).

I hope this helps clarify the calculation of uncertainty in x based on the given information. However, it is important to note that this is only an estimation and the actual uncertainty may vary based on the specific experimental conditions and precision of measurements.
 

What is the formula for a=exp x?

The formula for a=exp x is a = ex, where e is the mathematical constant approximately equal to 2.71828.

What does an uncertainty of 3% mean in relation to a=exp x?

An uncertainty of 3% means that the actual value of a could be 3% higher or 3% lower than the given value of a=exp x. This uncertainty is due to measurement error and other factors that may affect the accuracy of the value.

How is uncertainty in a=exp x calculated?

Uncertainty in a=exp x is typically calculated using the formula Δa = a * Δx, where Δa is the uncertainty in a, a is the given value of a=exp x, and Δx is the uncertainty in x. In this case, Δa = 0.03 * a, since the uncertainty is given as 3%.

Can the uncertainty in a=exp x ever be eliminated?

No, the uncertainty in a=exp x can never be completely eliminated. However, it can be minimized by improving measurement techniques and reducing sources of error.

How does the uncertainty in a=exp x affect the overall results of an experiment or study?

The uncertainty in a=exp x can affect the precision and accuracy of the overall results. A larger uncertainty may lead to a wider range of possible values for a, which can make it more difficult to draw conclusions from the data. It is important to consider and report the uncertainty in any scientific study to accurately represent the results.

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