Posted: Feb 22, 2012 8:12 am
E and the Natural Logarithm LN
One of the numbers that comes up a lot in physics, is e and its associated natural logarithm ln. For both of these I will again point you to the Wolfram site to read upon the basics:
e at Wolfram
Natural logarithm ln
e is another irrational number like π; it comes up a lot if you are studying physics or mathematics, and I suggest that you read at least the basics on e. Maybe someone else might take up a discussion on the various mathematical irrational numbers like e and π.
In mathematics e is a lot of times interchanged with exp as a symbol. Let's first see the functions:
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Then the derivatives will be:
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If you will notice, in the derivative of the natural logarithm, the constant a does not feature anywhere. If you know anything about logarithms, then you will know that:
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ln(a) is itself a constant, and so its derivative is 0. So we are left with the derivative of the second term, which is ln(x).
Some basic mathematical tricks with the above functions:
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