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Euler's number. Why is Eule's number "e" the basis of natural logarithm functions

Sumaanyu Maheshwari

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Document from the year 2016 in the subject Mathematics - Miscellaneous, grade: A, , course: IB Math HL, language: English, abstra...

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Document from the year 2016 in the subject Mathematics - Miscellaneous, grade: A, , course: IB Math HL, language: English, abstract: When the concept of logarithms was first introduced to me, a plethora of questions revolved around my mind. My inquisitiveness compelled me to think and ask questions as to where are the practical applications of logarithms, why do we take different bases of these functions and what is the need for natural logarithms. Amongst these questions, one particularly intrigued me: why is e particularly the base of the natural logarithm. Why out of all numbers that exist did we choose e as the base of the natural logarithm function? I was fascinated by why taking the base e made the normal logarithm a natural logarithm. Therefore, to quench the curiosity of many others like me, I will show through this paper that why e is the correct choice for the base of exponential and natural logarithm functions. I shall also be exploring the most important property of e, via this paper.