How was the concept of $\ln(x)$ found before the man knows that it is the area under hyperbola or it is related to the power of $e$ (base of logarithm). How did Napier compute the value of $e$ or $\ln(x)$ before the concept of power of numbers was used in math?

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    $\begingroup$ See Florian Cajori's 7-part series of papers History of the exponential and logarithmic concepts in American Mathematical Monthly, Volume 20 (1913), pp. 5-14, 35-47, 75-84, 107-117, 148-151, 173-182, 205-210. $\endgroup$ – Dave L Renfro May 15 '19 at 7:22
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    $\begingroup$ Before the invention of the logarithms, long multiplications used to be performed by the prosthaphaeresis method, based on the product-to-sum trigonometric formulas. In fact, these were already logarithms, but in the imaginary domain ($e^{ia}e^{ib}=e^{i(a+b)}$). $\endgroup$ – Yves Daoust May 15 '19 at 7:30
  • $\begingroup$ Powers of numbers were known long before Napier. $\endgroup$ – Yves Daoust May 15 '19 at 7:37
  • $\begingroup$ See Brian Rice & Enrique González-Velasco & Alexander Corrigan, The Life and Works of John Napier (2017, Springer). $\endgroup$ – Mauro ALLEGRANZA May 15 '19 at 7:41
  • $\begingroup$ If the concept of power of numbers were known before Napier,there were no use for it unless it is applied in logarithm $\endgroup$ – user359791 May 15 '19 at 7:47