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The product cd or quotient c/d came from looking up the antilogarithm of the sum or difference, also via the same table:
A person can use logarithm tables to divide two numbers, by subtracting the two numbers' logarithms, then looking up the antilogarithm of the result.
Fold number is definied in ISO 5626:1993 as the antilogarithm of the mean folding endurance:
The inverse function is the natural logarithm ln(x); because of this, some old texts refer to the exponential function as the antilogarithm.
These are converted to transmission values (by taking the antilogarithm of each absorption) and inserting the results into ASTM E-308.
For manual calculations that need precision, performing the lookups of the two logarithms, calculating their sum or difference, and looking up the antilogarithm is much faster than performing the multiplication by earlier ways.