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    Logarithms: adding ten
    From: Ed Popko
    Date: 2019 May 11, 03:44 -0700

    Logarithms were used extensively in navigation computations in the 19th century.


    The logarithm, base 10 for example, of the Sine of 45 degrees is a decimal and it's logarithm is a negative decimal:
    SIN(45) = .707107  and its log is -0.150515.

    Logarithms eliminated the multiplication and division, operations now acomplished with addition and subtraction. However, in the 19th century, there was a 'distaste' for doing calculations with negative numbers.  A common practice was to add 10 to the log and use that form for computation, thus:
    Sin(45) .707107
    Log      -0.150515
    Log+10    9.849485  (adding 10 to a log is adding 10^10 or 10,000,000,000 to the common number)

    To be consistent, all logs in the algorithm had to be treated the same way. At the conclusion of the sum of a number of such logs, the 10's were rejected and the log+10 looked up in a table to find the anti-log angle in standard notation form.

    What is the Log+10 form of a logarithm called?

    Ed

       
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