# Question about base e

1. Dec 29, 2013

### vanceEE

Why does $$e^{C} = Ce ?$$

2. Dec 29, 2013

### 1MileCrash

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
3. Dec 29, 2013

### vanceEE

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
4. Dec 29, 2013

### vanceEE

Ok thanks

5. Dec 29, 2013

### 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.