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Is it Possible to solve Exponential Equations like these?

  1. Apr 15, 2016 #1
    1. The problem statement, all variables and given/known data
    Hi, I have come across this equation in modelling exponential growth and decay. I am wondering if it is possible to solve it algebraically or not?

    2. Relevant equations
    8000-1.2031 * e^ (0.763x)=(0.5992×e^0.7895x)

    3. The attempt at a solution
    Brought all e^(ax) values to one side, however beyond that step I am really not sure of where to go, have looked at the problem for several hours without any results, any help would be appreciated.
     
  2. jcsd
  3. Apr 15, 2016 #2

    SteamKing

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    In general, there is no algebraic method to solve such equations since they are transcendental rather than algebraic by nature.

    Only a numerical or graphical solution can be obtained. Iteration using different trial values of x is probably the quickest way to find a solution here.
     
  4. Apr 16, 2016 #3
    Hi SteamKing, thankyou for your answer, I have learnt something from that.
     
  5. Apr 16, 2016 #4

    haruspex

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    In this particular equation, you can easily see that the second exponential expression is likely to be about half the first, so x must be about 10.
    You could then rewrite the .7895x as .763x+.0265x, or approximately .763x+0.265. That should get you to a reasonably accurate answer. You could redo that with the more accurate x value as a check.
     
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