Exponents and Logarithms

What is e in terms of logarithms?

No, e is not the code name in a James Bond movie. When talking about logarithms (or logs), in the majority of mathematical circles, it means the base of the natural logarithm. It is yet another irrational, transcendental number (such as pi, or π) that has a plethora of names: It has been called everything from the logarithmic constant and Napier’s number to Euler’s constant and the natural logarithmic base. One of the best ways to define e is to use the expression (1 + x)(1/x); e is the number that this expression approaches as x gets smaller and smaller. Substituting in values for x gives you the idea: if x = 1, the result is 2; if x = 0.5, the result is 2.25; when x = 0.25, the result is 2.4414…; if x = 0.125, the result is 2.56578 …; if x = 0.0625, the result is 2.63792…; and so on. This is why approximations are often used in solving equations using e.


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