Invest in the Future of Mathematics You've probably heard of Euler's number, e. It can be calculated through the expression “e=2.718281828”. The symbol is called the natural logarithm, which describes how if you have a number, "x," then raising that number to some power "n" returns an exponential value with the property that it is bigger than one when put to very large values of "n." For instance, if I raised 5 to two power (squared), this would equal 25 or 32 if I raised it to three or four power respectively. If we take a look at the expression, "e=2.718281828," it is an interesting number as it is very close to 1, yet it will never equal 1 as you can see from the following expression: "e^1=2.718281828.." If you multiply both sides of this equation by "n," you get 4.085956.... This is also equal to e raised to the fourth power which is equal to six-point-six-five-six-five... But 6 does not divide into 3, so this evaluates out to 2.718281828 which is what you would expect for "e. ” The number e has appeared throughout history to prove or disprove mathematical and physical theories. Apparently, it was used in ancient Rome by both Pliny and Lucretius as a fractional value for the rate of interest an investor could expect. It can be found in many major developments in mathematics and science; it is also the base of the natural logarithm function (e~ =2.718281828). Although e is commonly used as a base value and is often quoted as a natural logarithm, the value of the number is irrelevant to its use in calculations. Its utility does not lie in its value but rather in the manner in which it is used. For example, we can calculate an exponential as such: How I came up with this? I first figured out that if I made "n" equal to 1, then "e^1=2.718281828" assuredly holds true because I am multiplying the left and right sides of the equation by 1. So far so good. Pause for a moment and look at the expression: 2.718281828... * 1 = 2.718281828... Now I will add one to both sides of the equation: 2.718281828... + 1 = 3.718281828... Now I will take away unity which we can do by multiplying both sides of the equation by "e~": e~ * (2.718281828.. - 1) = e~. To finish off my reasoning, I found that: e~ - 0 = e~ and 2e~ + 0 = e~ and therefore, 3e^x-1=0 is true for any value of x which is positive or equal to zero.
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