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

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    Uncertainty
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Discussion Overview

The discussion revolves around the calculation of uncertainty in the variable x, given the relationship a = exp(x) and a known uncertainty in a. Participants explore the implications of error propagation and the correct interpretation of units in this context.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant proposes that the absolute uncertainty in x can be calculated using the formula involving the natural logarithm of a.
  • Another participant challenges the initial claim by stating that x cannot have units of mm and that the value of a = 2 does not correspond to x = 3.
  • A participant suggests using error propagation by rewriting the expression as x = ln(a) and finding the derivative with respect to a.
  • There is a question raised about whether the absolute uncertainty in x is equal to the percentage uncertainty in a.

Areas of Agreement / Disagreement

Participants express differing views on the correct units for x and the relationship between a and x. The discussion remains unresolved regarding the calculation of uncertainty in x.

Contextual Notes

There are limitations regarding the assumptions about units and the correspondence between values of a and x, which have not been fully clarified.

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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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.
 
so dx = da/a?

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

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