# How was logarithm discovered? [duplicate]

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?

• 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. – Dave L Renfro May 15 '19 at 7:22
• 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 ($e^{ia}e^{ib}=e^{i(a+b)}$). – Yves Daoust May 15 '19 at 7:30
• Powers of numbers were known long before Napier. – Yves Daoust May 15 '19 at 7:37
• See Brian Rice & Enrique González-Velasco & Alexander Corrigan, The Life and Works of John Napier (2017, Springer). – Mauro ALLEGRANZA May 15 '19 at 7:41
• If the concept of power of numbers were known before Napier,there were no use for it unless it is applied in logarithm – user359791 May 15 '19 at 7:47