Is it Possible to solve Exponential Equations like these?

[Alex Myhill]

Homework Statement

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?

Homework Equations

8000-1.2031 * e^ (0.763x)=(0.5992×e^0.7895x)

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.

 

[SteamKing]

Homework Statement

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?

Homework Equations

8000-1.2031 * e^ (0.763x)=(0.5992×e^0.7895x)

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.

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.

 

[Alex Myhill]

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

 

[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.