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

[Loren Booda]

How can one explain the Napierian logarithm without calculus?

 

[Hurkyl]

What's wrong with Mathworld's page?

 

[Loren Booda]

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?

 

[Hurkyl]

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.