Converting Error in Log2 Form for Arbitrary Base

AI Thread Summary
To convert error for log2 transformations, the formula used is dy = (1/ln(2))(deltax/x), where deltax is the standard deviation and x is the mean. The discussion began with a query about converting error from mean values to log2 form, specifically for arbitrary bases. The user initially struggled to recall the correct method but later figured it out. The relationship between logarithmic bases is established through the natural logarithm, leading to the derived error formula. This method allows for accurate representation of data in log2 form while accounting for error.
dipluso
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Hi,

I am trying to represent my data in log2 form rather than "fold change" and I am embarrassed to say I can't remember how convert the error.

For example, I have x=3.96 (mean), deltax=0.28 (standard dev).

Thus, log2(x)=0.598.

But how do I convert the error??

I know how to do it for log10: 0.434(deltax/x) but I can't for the life of me remember how to derive it for an arbitrary base.

Any help/pointers much appreciated.

Thanks!
 
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Duh, figured it out.

For y=ln(x), error dy=dx/x

since lob(x) base b = ln(x)/ln(b)

Then for y=lob(x) base b , error is dy=(1/ln(2))(deltax/x)

Done. Cheers, -Alex
 
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