# Improving the NonlinearModelFit

I've been trying to fit logarithmic function to the data below:

d1 = {{3457, 4.22}, {3000, 4.33}, {2500, 4.35}, {1200, 4.43}, {600, 4.68}, {300, 5.8}, {150, 8.07`}}

I used the following code for the fitting:

nmf1 = NonlinearModelFit[d1, a + b Log[x], {a, b}, x]

g1 = ListPlot[d1];
g2 = Plot[nmf1[x], {x, 0, 3500}];
Show[g1,g2]

where g1 is the $$ListPlot$$ of the data d1. I got the below fit.

I am wondering how to improve this fit. The expected function is the natural logarithm, although in this case I managed to do a much better fit with the 1/x. Additionally, I don't have an initial guess at the parameters, which I could use. Any ideas?

Thank you all for help!

• Just an observation: your parameter c is redundant. – b.gates.you.know.what Jan 30 at 8:47
• Right. Thanks for pointing this out. – Nejc Kejzar Jan 30 at 8:48