# Is it Possible to solve Exponential Equations like these?

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1. Apr 15, 2016

### Alex Myhill

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. Apr 15, 2016

### SteamKing

Staff Emeritus
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.

3. Apr 16, 2016

### Alex Myhill

Hi SteamKing, thankyou for your answer, I have learnt something from that.

4. Apr 16, 2016

### haruspex

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.