Feynman apparently is in the domain literature for numerical analysis of an algorithm which computes the logarithm of a number between 1 and 2. Any such number is a unique product of factors of the form (1 + 2 ** -k) for integral k. Logarithms of all such factors fit in a table of modest size. Determination of the sequence of k-s can be done with shifts and subtracts.
Here's a Tcl coding that illustrates the algorithm:
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