Need something solving PROBLEM AHOY

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The user seeks assistance with an algebraic equation involving exponentials, specifically rearranging the equation 1 = -((e^ZL) + (e^Zw)) for Z. It is noted that there is no closed-form solution for Z when L and w are arbitrary. However, if L and w are specific values, such as L = 3500 and w = 24, the problem can be approached differently. The discussion emphasizes the challenge of finding a general solution while also addressing the complexities of working with real and complex numbers. Ultimately, the user is looking for a method to solve the equation for various values of L and w.
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Need something solving! PROBLEM AHOY!

Hi there,

Im in dire need of a problem solving because i really cba to do it at this time of nite and need sorting by 2moz morning... putting my faith in PF here... I don't think its too diff I just havnt done any algebra for a while and need some assistance.

Need this rearranging for Z:

1=-((e^ZL)+(e^Zw))

Any help much appreciated!


Regards

Sol
 
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If L and w are arbitrary (assuming multiplying Z in the exponents) there is no closed form solution for Z.
 


ok mate, well is there any way i can find it if L and W arnt arbitrary?
 


In real numbers, the problem is immediate: no linear combination of powers of e will ever equal -1.

In complex numbers, L = W would make things a lot simpler, but that's trivial...
 


Ok, well in this instance i need it solving for w = 24 and L = 3500, but i would like a general solution so i can apply any values for L and w
 

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