How to solve summation of exponential equations

[fenixtx423]

Hello all

Is there any way to solve this equation for X? I cannot seem to find a solution

y = c₁e^c₂X + c₃e<sup>c₄X

Thanks in advance</sup>

 

[HallsofIvy]

Just as there is no way to simplify \(\displaystyle log(x)+ log(y)\), there is no algebraic way to solve \(\displaystyle y= c_1e^{c_2x}+ c_3e^{c_x}\) except in special cases. For example, if \(\displaystyle c_2= 1\) and \(\displaystyle c_4= 2\), so that the equation is \(\displaystyle y= c_1e^x+ c_3e^{2x}\), we can let \(\displaystyle z= e^x\) so that the equation becomes \(\displaystyle y= c_1z+ c_3z^2\) or \(\displaystyle c_3z^2+ c_1z- y= 0\). That can be solved for z using the quadratic equation and then \(\displaystyle x= ln(z)\).

But that is, as I said, a special case.

 

[fenixtx423]

Thanks for the quick response. I will take a closer look at the data sets I am working with to see if there is any relation between the constants.