Podcast #128: We chat with Kent C Dodds about why he loves React and discuss what life was like in the dark days before Git. Listen now.

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LogPlot plots $\log y$ vs. $x$, so the slope in the plot is given by $$m = {d \over dx} \log y = {dy/dx \over y} \,.$$ If you let f be your function, whether that is an InterpolatingFucntion[...][x] or some other function, the slope of the tangent to use in the LogPlot at x == x0 will be given by D[f, x]/f /. x -> x0 Note that the tangent "line" ...


Sorry, I didn't realize that you linked to the data in your post, but as @Roman noted, the InterpolatingFunction seems broken. Anyhow, I managed to extract enough to find another problem besides @Roman's comment to use LogPlot[Exp[linearpart], ...]. Specifically, your Table doesn't include x-coordinates, so Fit assumes they are 1, 2, 3, ... Instead try: ...

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