# Thread: How to solve a complex exponential equation with one unknown???

1. ## How to solve a complex exponential equation with one unknown???

I need to solve this equation for 'B'. I am having trouble rearranging the equation to achieve a 'B=' answer. Can someone help me rearrange this equation to solve for B?

0=((DCRMg) - (DCRMgAl)) ∗ e^(-B∗((ρMg)+(ρAl)))+ ((DCRMgAl )- (DCRAl ))∗e^(-2∗B∗(ρMg))+((DCRAl) - (DCRMg)) e^(-B∗((ρMg)+(ρMgAl)))

2. ## Re: How to solve a complex exponential equation with one unknown???

replacing various constants with single letters, this is $a- be^x+ ce^{2x}+ de^x= 0$

where $a= (DCRM_g- DCRM_gIa)e^{\rho RAI}$, $b= (DCRM_gAI- DCRAI)$, $c= (DCRAI- DCRM_g)e^{\rho M_gAI}$, $d= (DCRAI- DCRM_g)e^{\rho M_gAI}$ and $x= B(\rho M_g)$.

If we further write $y= e^x$ that equation reduces to $cy^2+ (d- b)y+ a= 0$ which can be solved for y using the quadratic formula. Once we have $y= e^x$, $x= B(\rho M_g)= ln(y)$ and then $B= \frac{ln(y)}{\rho M_g}$.

3. ## Re: How to solve a complex exponential equation with one unknown???

Thank you for your help HallsofIvy. Could you possibly re-write the equation as 'B=.......' I am struggling with this....
'

4. ## Re: How to solve a complex exponential equation with one unknown???

I have been recently told that this equation must be solved using Excel Solver. I have no idea how to use this program in order to calculate B.
I have created an excel formula relative to the above equation, but I am stuck at this point. Are you able to show me how you would solve the equation for B in Excel Solver?

=(B50-C50)*EXP(-B*($H$44+$I$44))+(C50-D50)*EXP((-2*B($H$44)))+(D50-B50)*EXP((-B($H$44+$J$44)))

5. ## Re: How to solve a complex exponential equation with one unknown???

You can use exact solutions given here in your Excel module.