Posted by Adam on April 15, 2002, at 11:07:23
In reply to Adam, I have no idea what you did! what is ''e''? (nm) » Adam, posted by Janelle on April 13, 2002, at 1:45:04
Hi, Janelle,
e is the base of the "natural logarithms" and is sometimes called "Euler's number". It has a value of aprox. 2.7183. When you write ln, that's just the symbol or "operator", which tells you to take the "natural log" of something. Any scientific calculator will allow you to take the natural log of a number just by hitting the ln key after entering that number.
So, if I write something like e^kt, that means I'm taking 2.7183 to the power of whatever kt is. If k equals 3 and t equals 2, then e^kt equals 2.7183 to the power of 6, or 403.445. Now, if I entered ln 403.445 into a calculator and hit the ln key, the answer would be very close to six (it's not quite six because I've rounded off a few numbers to the right of the decimal point...otherwise, it would be exactly six).
So, taking e to the power of some number is sort of the reverse of taking the natural log of the result of that calculation. For example, let's use the "base-ten" logs. 10^2 equals 100. The log(10) of 100 is 2. Now again for the natural logs: e^2 equals 7.3892, and ln 7.3892 = 2.
OK, so why would you take the "natural log" of something when you could use a more convenient log system, like base ten? That's kind of a complicated question to answer. I bet Elizabeth could do a better job than me. Anyway, in calculus, you can do operations on equations following certain rules, which give you, say, the area under the curve described by that equation. This works in a relatively straightforward manner except for equations like 1/x (equations where x is to the -1 power). For those equations, taking the log base e of x from 1 to whatever the value of x is gives you this information. Euler's number is kind of this amazing tool, then, for doing such calculations, that arises naturally, if you will. I suppose the value of e means something deep about the universe, but it is well beyond my intelligence to fathom what that could be.
poster:Adam
thread:101843
URL: http://www.dr-bob.org/babble/20020408/msgs/103123.html