Log base e versus log base 10 for semilog plot, how do I recognize the type of curve my data fits?

Question

If I have a curve (with some noise) that looks like logarithmic growth, how can I find out whether I should use Log base 10 or Log base e on the y axis in order to estimate a linear fit on the semilog plot?

Answer 1

Any logarithm is just a constant multiple of the natural logarithm. We can see this by the change of base formula $\log_a(x)=\frac{\log(x)}{\log(a)}$, with the logarithms on the right being any base. Basically, $\log_{10}(x)=\frac{1}{\log(10)}\log(x)$, so the only difference the choice of base for your logarithm is the scaling, which you can change after.

So choose whichever you'd like.