# Definition:Logarithm/Historical Note

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## Historical Note on Logarithm

The initial invention of the logarithm was by John Napier, who used a base $\dfrac {9 \, 999 \, 999} {10 \, 000 \, 000}$.

William Oughtred, who invented the slide rule, added a table of natural logarithms to his English translation of Napier's book.

In $1685$, John Wallis established that logarithms can be considered as exponents.

In $1694$, Johann Bernoulli made the same discovery.

Logarithms in their modern form are as a result of the original work done by Leonhard Paul Euler.

Euler was the first one to create a consistent theory of the logarithm of a negative number and of an imaginary number.

He also discovered that the logarithm function has an infinite number of values for a given argument.

## Sources

- 1972: George F. Simmons:
*Differential Equations*... (previous) ... (next): $\S 3$: Appendix $\text A$: Euler - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $9,999,999$ - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.21$: Euler ($\text {1707}$ – $\text {1783}$) - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $9,999,999$