R Coding Questions (Fitting log SLR onto normal scale)

Hey guys I'm having trouble with R and which codes to use(Newbie):

So I have some data, I've performed a simple linear regression (SLR), however I found that this doesn't give me the relationship I want.

So I performed another SLR analysis using the log (base 'e') of both the variables and it seems to be a better fit.

My question is that what codes do I use to include plot by log SLR onto my original data (into a smooth curve) i.e. how do I fit the new data, with a log scale, onto my original data.

From what I understand I use the following:
1) plot(x,y) <-- Original data
2) ???? lines(fitted(exp(____)))? <-- Not sure about what to do here

If you guys could help me that would be great