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****=((DCR****Mg***) - (DCR**MgAl**)) ***∗ e^(-B∗((ρ****Mg****)+(ρ****Al****)****))+ ***((DCR**MgAl** )- (DCR**Al ***))∗****e^(-2∗B∗(ρ****Mg****))+****((DCR***Al**) - (DCR**Mg**)) ***∗****e^(-B∗****((****ρ****Mg****)****+****(****ρ****MgAl****))****)**

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

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

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

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

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....

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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)))

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

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

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