Converting Errors for Logarithmic Graphs for Scientists

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SUMMARY

This discussion focuses on converting errors for logarithmic graphs, specifically in the context of a lab report involving the equation ln(I_REF/I) = (-hv/k)(1/T_REF - 1/T). The user seeks guidance on how to calculate the errors in Log(I) and Log(T) when given errors in I and T. It is established that the behavior of errors differs from the general behavior of values, suggesting that separate graphs may be necessary for clarity in representation.

PREREQUISITES
  • Understanding of logarithmic functions and their properties
  • Familiarity with error propagation techniques
  • Basic knowledge of graphing in scientific contexts
  • Proficiency in using graphing software (e.g., Excel, OriginLab)
NEXT STEPS
  • Research error propagation in logarithmic functions
  • Learn how to use Excel for creating graphs with error bars
  • Explore OriginLab for advanced graphing techniques
  • Study the principles of separate graphing for different data sets
USEFUL FOR

Students, scientists, and researchers involved in data analysis and graphing, particularly those working with logarithmic relationships and error analysis in their lab reports.

Fluorescent
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I think this is probably the right place to put it, didn't really fit anywhere else.

I've got the joyless task of writing a lab report at university and need to put a graph in it, ideally with error bars. I don't have a problem with error bars normally, but I'm coming unstuck about what to do in this case.

I have the equation: ln\frac{I_{REF}}{I} = \frac{-hv}{k}[\frac{1}{T_{REF}} - \frac{1}{T}]. This is in the form y=mx.

If I were to have values for the errors in I and T, how would I convert these into the errors of Log(I) and Log(T) and thus graph them?
 
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I don't see your logarithm on the right, but you can handle them as usual just take the logarithm beforehand, except the behaviour of errors is different from the general behaviour of the value. In that case two separate graphs might be useful.
 

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