Subtraction of Exponentials?

Question

I know how to work subtraction of logarithms, but I am not sure if exponentials work in the same way or the inverse way. I've tried everything and I can't get it to work. Here's my example if you could walk me through the steps:

e^2x - 3e^x + 2 = 0

Answer 1

There is, in general, no way to simplify subtraction of exponentials (exponentiation does not distribute over addition). In order to solve this equation, you make a substitution of variables -- u=e^x. Then this becomes a quadratic equation:

u²-3u+2=0

Which factors as:

(u-1)(u-2)=0

So u=1 or u=2. But u=e^x, so:

x=ln 1 or x=ln 2

Answer 2

Subtracting Exponential Functions

Answer 3

You can't directly add or subtract exponents. However, if you're trying to solve this equation for x, notice that if you let t = e^x, the equation becomes: t^2 - 3t + 2 = 0. You can solve this quadratic for t, and then find Ln(t) to give you back x (since t = e^x).