# Exponential manipulation

1. Jan 14, 2010

### winterwind

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. Jan 14, 2010

### rock.freak667

Why can't you use that? What is the integral expression you are talking about?

3. Jan 14, 2010

### winterwind

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
4. Jan 15, 2010

### vela

Staff Emeritus
You're overthinking it. Use the substitution $x=\nu(h/kT)$.

5. Jan 15, 2010

### Bohrok

eab = (ea)b and ea is just a constant.

Then ∫bx dx = bx/ln(b) + C

6. Jan 17, 2010

### winterwind

Thanks! This is it.