The exception holds only for the middle node of even harmonics, which is always precisely at the midpoint of the string over the 12th fret. One way to find the nodes would be to measure the active length of the string with a meter stick, divide the length by the desired harmonic, and take multiples of this distance to each successive node. Well, that is almost right, and actually the approximation is pretty good for the 2nd, 3rd, and 4th harmonics. We can find improved locations for the 5th harmonic, though, and in principle we can find the location relative to the frets for any node of any harmonic we might want. I will omit the theory behind the formula, and just give you the start and end points.
Interested readers can fill in the details.
You must use the same base for both log function evaluations. Except for this exact answer, the results will not be integers. The parts after the decimal point should be interpreted as a fraction of the distance to the next fret, as if you were interpolating on a ruler. In principle we should correct for the shrinking scale within the span from fret to fret, but the error is smaller than the contact area of your finger on the string. The numbers in parentheses are correct node locations, but they are shared by lower harmonics.