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I want to find a concise way of asking the following, so that I can re-post it.

I have a limited set of data from which I would like to find a function that approximates the data. That is, if you plot the following [x:y]:

1:0, 2:1, 3:7, 6:8, 7:16, 9:19, 18:20, 25:23, 27:111, 54:112, 73:115, 97:118, 129:121, 171:124, 231:127, 313:130, 327:143, 649:144, 703:170, 871:178, 1161:181, 2223:182, 2463:208, 2919:216, 3711:237, 6171:261, 10971:267, 13255:275, 17647:278, 23529:281, 26623:307, 34239:310

the resulting graph appears to be roughly logarithmic. Is there a way to generate a function such that for each x from the data it will produce a y "close" to the expected y value from the data.

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    In statistics, this is called nonlinear regression, see Wikipedia, http://en.wikipedia.org/wiki/Nonlinear_regression, which also e$x$plains that nonlinear problems can be transformed to linear problems if there is reason to believe that there is, e.g., a logarithmic dependence.2011-06-13

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Perhaps you'll want to consider Logarithmic Regression.

EDIT: This very easy to use page allows you to work out logarithmic regressions.

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    Result: y = 31.78303295ln(x) - 36.17569359 Thank you very much!2011-06-13