1. [SOLVED] Sum of exponentials

Hi folks,

This is not for "homework" per se, it's actually for work - I'm trying to model something. I won't bore you with the details, but the basics of the problem boil down to being able to reduce the expression:

e^(ax) + e^(bx)

To a single term. I assumed that I may be able to express it as

e^(cx)

and tried to find the value of c that satisfied the first expression. However, this required that the value of c varied with x, so it seems that assumption was wrong.

Anyone know how to solve this problem?

2. Can you make (using arbitrary numbers) (e^2x) + (e^3x) into a single term? I'm not quite certain that you can.

e^2x + e^2x would just be 2e^2x, but with different exponents, I don't think too much can be done.

but wait for someone much smarter than me to come correct me hehe

3. Yes you're right, you can't collect them into a single term.

You might be confused with the index law for multiplication...

$a^m \times a^n = a^{m + n}$.

4. Ok, it is as I feared. This invalidates some basic assumptions about the model, which is quite useful to know!