How does Napier's logarithm make computing powers easier without calculus?

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Discussion Overview

The discussion revolves around the nature and utility of Napier's logarithm, particularly in the context of computing powers without the use of calculus. Participants explore historical aspects, practical applications, and theoretical implications of logarithms and slide rules.

Discussion Character

  • Exploratory, Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant asks how to explain Napierian logarithm without calculus, indicating a desire for a conceptual understanding.
  • Another participant questions the accuracy of Mathworld's page, suggesting potential inaccuracies or misunderstandings in the representation of Napier's work.
  • A participant raises a question about the significance of the power of 7 in Napier's tables, speculating it may be an artifact of historical context and inquires about the possibility of designing a slide rule that utilizes logarithms of logarithms for calculations.
  • It is noted that Napier's logarithm differs from modern logarithms, with a participant suggesting that the choice of 7 in his tables was likely for numerical convenience related to specific numbers of interest.
  • One participant explains that powers can be computed using a slide rule by applying the property log(a^b) = b * log(a), emphasizing the multiplication capability of slide rules.

Areas of Agreement / Disagreement

Participants express differing views on the historical context and practical applications of Napier's logarithm, with no consensus reached on the significance of the power of 7 or the accuracy of external resources like Mathworld.

Contextual Notes

There are unresolved questions regarding the historical significance of specific numerical choices in Napier's work and the limitations of current representations of logarithms compared to Napier's original concept.

Loren Booda
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How can one explain the Napierian logarithm without calculus?
 
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What's with the seemingly arbitrary power of 7; is that an archaic artifact of Napier's? Can one design a slide rule, in theory, that calculates powers by addition of the logarithm of logarithms?
 
Napier's logarithm isn't the logarithm we use today -- I would assume the 7 made his tables of logarithms numerically convenient for the numbers of interest.


You can compute powers with an ordinary slide rule:

log (a^b) = b * log a

and we know how to multiply with a slide rule.
 

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