Trouble interpolating data on semi-logarithmic chart

Is that 3.65 an eyeballed number, or can you explain you came up with that?

The 3.95 appears to come from linear interpolation using y=mx+b
The 4.06 appears to come from linear interpolation using ln(y)=mx+b
Perhaps you are looking for linear interpolation using y=ln(x)+b (which gives me 3.76).

I expect that, if you figure out exactly what kind of equation to use for the interpolation, you will get the answer you want. At this point, it looks to me like you need to figure out what kind of equation is the best one to use for the kind of data you have.

I basically used the same equations you did, though I often get rid of the functions and just spell it out.

3.95 =FORECAST(F12,A13:A14,B13:B14) -- basic linear interpolation with no transformation

4.06 = INDEX(LINEST(A13:A14,LN(B13:B14)),1)*LN(E12))+INDEX(LINEST(A13:A14,LN(B13:B14)),1,2) -- basic linear interpolation, but transforming y to be LN(y). Usually, rather than using two instances of the LINEST() function to return m and b, I will usually simply use a point-slope form of the equation of a line (ln(y2)-ln(y1))/(x2-x1)=(ln(y3)-ln(y1))/(x3-x1) fill in the known variable and solve for the desired unkown.

3.75 is similar to 4.06, only applying the =LN() transformation to the x values instead of the y values (y2-y1)/(ln(x2)-ln(x1))=(y3-y1)/(ln(x3)-ln(x1)).

So, while I could have used the INTERCEPT() function had I wanted to, I rarely use the INTERCEPT() function.