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Question about base e

  1. Dec 29, 2013 #1
    Why does $$ e^{C} = Ce ?$$
     
  2. jcsd
  3. Dec 29, 2013 #2
    It doesn't..

    If C is an arbitrary constant, it is true that I can say:

    $$ e^{C} = e * e^{C-1} = C_{2}e $$

    Because $$ e^{C-1} $$ is just some other constant. But it is not the same as C, it is a new constant.
     
    Last edited: Dec 29, 2013
  4. Dec 29, 2013 #3

    But $$e^{x^2+C} = De^{x^2} $$ are we just considering e^C to be an arbitrary constant since it is a number multiplied by a number?
     
    Last edited: Dec 29, 2013
  5. Dec 29, 2013 #4

    Ok thanks
     
  6. Dec 29, 2013 #5

    Mark44

    Staff: Mentor

    Probably already answered, but here are the details.
    ex2 + C = ex2 * eC = D ex2, where D = eC.

    Your question is really about the properties of exponents, and not specifically about the natural number e. The basic property here is am + n = am * an.
     
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