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

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Napier's logarithm simplifies power calculations by transforming multiplication into addition, making it easier to compute powers without calculus. The discussion critiques Mathworld's explanation and questions the significance of the power of 7 in Napier's tables, suggesting it may have been chosen for numerical convenience. It is noted that Napier's logarithm differs from modern logarithms, raising questions about its historical context. Additionally, the feasibility of designing a slide rule that utilizes the logarithm of logarithms for power calculations is explored. Overall, the conversation emphasizes the practical applications of Napier's logarithm in computational methods.
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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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