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Math Help - How to solve a complex exponential equation with one unknown???

  1. #1
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    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)))
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  2. #2
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    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}.
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    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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  4. #4
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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)))
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  5. #5
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    Re: How to solve a complex exponential equation with one unknown???

    You can use exact solutions given here in your Excel module.
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    Re: How to solve a complex exponential equation with one unknown???

    The link didn't work...
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