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What was John Napier's motivation to introduce the logarithmic function?

It neither makes the calculations easier nor accurate (at least for me). How could people think of its importance even before Calculus came into play and showed its connection with the exponential function or, area under the graph $\dfrac{1}{x}$ ?

user571036
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  • @ParclyTaxel I saw that post, wasn't satisfied with the answers. So, reposted it. – user571036 Jul 12 '18 at 14:13
  • What do you mean by "It neither makes the calculations easier nor accurate" for you? What exactly are you doing and how many times? – Cecilia Jul 12 '18 at 14:27
  • @Richard What about giving an example how logarithms make calculations easier? – user571036 Jul 12 '18 at 14:29
  • @user571036 When multiplying 1.2473 with 8.1637 you look them up in a table, add their logarithms and exponentiate the result (again with a lookup table). You can maybe multiply a few times by hand, but in the long run, lookup and addition provide a speedup and significantly fewer errors. – Cecilia Jul 12 '18 at 14:36
  • Also, mathematics and what mathematicians do is not just about "calculation". The natural logarithm and Napier number $e$ are interesting on their own (similar to how $\pi$ is interesting). For example, $\lim_{n\to \infty}(1+1/n)^n = e$, or $\sum_{n=0}^\infty 1/n!=e$, which (although today might seem obvious) is quite interesting. – Hamed Jul 12 '18 at 14:59
  • The exponential functions, $f(x)=b^x$, on a base $b$, are historically one of the first functions that were studied. And for good reason: If you know what $2^1, 2^2, \cdots$ is, the next natural question is to study $2^x$. Again naturally, you then inquire the inverse of a exponential function, which are the logarithmic functions. This is why logarithmic functions have been studied since forever ago. – Hamed Jul 12 '18 at 15:03

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