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Exponential manipulation

  1. Jan 14, 2010 #1
    1. The problem statement, all variables and given/known data
    I am working on a problem, and there is a small step I need help on:

    I have the expression eab, where a is a constant, and b is a variable. I need to separate a and b so I can pull out the expression b from an integral expression. Is there any exponent law or manipulation I can do algebraically that will allow me to get separate the constant a expression from the variable b expression?

    2. Relevant equations
    Rules of exponents, algebraic manipulations.


    3. The attempt at a solution
    There isn't any simple rule (i.e. xmxn = xm+n) that I can use to separate the two expression. I've tried moving the expression around, to no avail. Any help is appreciated!
     
  2. jcsd
  3. Jan 14, 2010 #2

    rock.freak667

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    Why can't you use that? What is the integral expression you are talking about?
     
  4. Jan 14, 2010 #3
    Unfortunately, that doesn't work, since the expression is eab. I would only be able to use that rule if it were eaeb. The constant a is multiplied to the variable b in the same exponential.

    The integral expression is: v3/[ev(h/kT) -1] where v is the variable, and (h/kT) is constant. Essentially, I need to get the expression in the form x3/(ex-1) , where then I can use a table of integrals to evaluate the integral. Is there a simple way to get the above expression into that form? In this case, v = x, so I am close, but there is the (h/kT) constant term in the exponential that still needs to be taken care of.
     
    Last edited: Jan 14, 2010
  5. Jan 15, 2010 #4

    vela

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    You're overthinking it. Use the substitution [itex]x=\nu(h/kT)[/itex].
     
  6. Jan 15, 2010 #5
    eab = (ea)b and ea is just a constant.

    Then ∫bx dx = bx/ln(b) + C
     
  7. Jan 17, 2010 #6
    Thanks! This is it.
     
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