log (a·b·c···) = log a + log b + log c···

and the series relation

logₑ(1 + h) = h - h²+h³-h⁴ + ···, │h│ < 1
234

The error in this series is less than the first neglected term. Now, the machine stores the base 10 logarithms (to 23 decimal places) of the following 36 numbers:

11.11.011.001
21.21.021.002
............
91.91.091.009

First, the number 49.3724 is examined in a counter called the Logarithm-In-Out counter, and the position of the decimal point is determined, giving the characteristic of the logarithm. The number 49.3724 has the characteristic 1. Next, 4 successive divisions are performed, in which the 4 divisors are (1) the first digit of the number, (2) the first 2 digits of the quotient, (3) the first 3 digits of the next quotient, and (4) the first 4 digits of the subsequent quotient; thus,

4.93724 = 1.23431
4
1.23431 = 1.02860
1.2
1.02860 = 1.00843
1.02
1.00843 = 1.00043
1.008

For simplicity we have kept only 6 digits, although the machine, of course, would keep 23. It is interesting to note that the machine is able to sense digits and thus determine the 4 divisors; this is an arithmetical and numerical process and one that cannot be done in ordinary algebra. We now have:

log₁₀ 49.3724 = 1 + log₁₀ 4 + log₁₀ 1.2 + log₁₀ 1.02
+ log₁₀ 1.008 + log₁₀ 1.00043

To compute log₁₀ 1.00043 to 21 decimals we use