Bit of a mathophobe. I have fit a regression to some data on a semi-log plot, and the resulting equation of the function is:
$$ y = e ^ {log_{10} x} + 1.024 $$
That seems overly messy and wrong to me, but I cannot figure out why (it's been a while since I did any proper maths, but something doesn't sit right with me)
Any input would be a great help!
Here's an image of the plot itself:
The fit curve works to reproduce the y variable in locations where only the x variable isn't present.
I have looked at your image and the blue curve seems to fit $f(x)=y=0.6+0.4 \;x^{1/ln(10)}.\;$Note that $\;e ^ {log_{10} x}=x^{1/ln(10)}$. The two constants can be adjusted for better fit. My fitted function gives $\;(x,f(x))\;$ data points $(1,1),(10,1.7),(100,3.6),(400,6)\;$ which you can compare to your data.