The questioner wanted a mathematical method to scale different logos so that the resulted sizes seem to be equal. There are few ways to drag the mathematics into the process:
A. Let one or more people to do the scaling for a large logo collection. Then a mathematician finds a computable "logo size measuring function" which is forced to match with the result.
B. One derives the logo size measuring function from some accepted perception theory
C. One takes his own ac-hoc logo size measuring function and uses it
The logos are scaled to give the same size when the selected logo size measuring function is applied.
Unfortunately A. and B. are beyond my capablities. But I can give some my own measuring functions:
M1: The amount of ink when the logo is printed as full black on white (or as well total colored area)
M2: Like M1, but the ink is weighted with the distance from the centerpoint of the logo. That's physically the inertial moment.
M3: The perimeter of the bounding box of the logo
Using M1 gives easily too much real estate for those logos which have only thin lines. M2 is better because even the thinnest line gets heavy weight when the line is far enough from the centerpoint. Unfortunately the practical calculation is tricky, but it can be done, if Photoshop is allowed.
M3 is easy. Only check the width and height of the bounding box in the infoline. You can add the width and height, no need to multiply by 2 if all logos are measured in the same way.
An example using M3: These logos are tried to draw approximately to the same size.
In illustrator summed widths and heights are 78mm for logo1, 76mm for L2 and 93mm for logo3. If we let L2 be as is, we must scale logo1 to (76/78) = 97% and L3 to (76/93) = 82%. The results:
M1 is skipped due its weakness. But M2 gets some attention. Weighting is possible in Photoshop. One can add a radial gradient with blending mode multiply and do the average blur. One color channel value in the averaged image is the measure. The result is the following:
We see that thick black gives remarkably less real estate than thin lines.
The scaling of the inertial moments are tricky. The right scaling is the cubic root of the ratio of the measures. Further details are skipped.