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Uncertainty propagation through logarithms

So, I've got a bunch of readings that I need to construct a log-log graph with (well actually I'm using ln). I've got all the uncertainties for the raw readings, but how should I go about calculating them for the values modified with the ln function?

First of all, is it possible to get the percentage uncertainties for the logs using those from the raw data? Or must I use absolute values with the logs and calculate the uncertainties 'from scratch' again? This is really confusing me, and the worst part is my teacher says we shouldn't even bother changing the percentage uncertainties when applying the logs! What should I do?
Original post by Phaidon
So, I've got a bunch of readings that I need to construct a log-log graph with (well actually I'm using ln). I've got all the uncertainties for the raw readings, but how should I go about calculating them for the values modified with the ln function?

First of all, is it possible to get the percentage uncertainties for the logs using those from the raw data? Or must I use absolute values with the logs and calculate the uncertainties 'from scratch' again? This is really confusing me, and the worst part is my teacher says we shouldn't even bother changing the percentage uncertainties when applying the logs! What should I do?


Answer here

http://phys114115lab.capuphysics.ca/App%20A%20-%20uncertainties/appA%20propLogs.htm
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Phaidon
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Original post by Stonebridge


Thanks very much for that link. As I have a bunch of values and aim to get a percentage uncertainty for the whole thing, should I use that method on whichever value would give me the greatest percentage uncertainty?
Impossible to say without knowing what you are doing exactly.
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Phaidon
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Original post by Stonebridge
Impossible to say without knowing what you are doing exactly.


Fair enough. And maybe you don't want to know exactly what I'm doing since it regards coursework... But one other thing - is it possible to find the uncertainty in the y-intercept of a linear graph without drawing a bunch of different lines of best fit?
Original post by Phaidon
Fair enough. And maybe you don't want to know exactly what I'm doing since it regards coursework... But one other thing - is it possible to find the uncertainty in the y-intercept of a linear graph without drawing a bunch of different lines of best fit?


You draw two lines. A best and a worst. The uncertainty is plus/minus the difference between the two. That's standard practice.
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Phaidon
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Original post by Stonebridge
You draw two lines. A best and a worst. The uncertainty is plus/minus the difference between the two. That's standard practice.


Alright then. So the worst can be steeper or shallower than the best? And can (or should) this also be used to get the uncertainty of the gradient?
Original post by Phaidon
Alright then. So the worst can be steeper or shallower than the best? And can (or should) this also be used to get the uncertainty of the gradient?


Yes to both.

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