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Math Help - [SOLVED] Sum of exponentials

  1. #1
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    [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?
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  2. #2
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    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
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  3. #3
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    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}.
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  4. #4
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    Ok, it is as I feared. This invalidates some basic assumptions about the model, which is quite useful to know!

    Thanks for your help.
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