Need something solving PROBLEM AHOY

  • Context: High School 
  • Thread starter Thread starter SolStis
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Discussion Overview

The discussion revolves around solving the equation 1 = -((e^ZL) + (e^Zw)) for Z, with a focus on both specific values for L and w as well as a general solution applicable to any values. The context includes algebraic manipulation and potential solutions in real and complex numbers.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant expresses a need for assistance in rearranging the equation for Z, indicating a lack of recent practice with algebra.
  • Another participant notes that if L and w are arbitrary, there is no closed form solution for Z.
  • A subsequent reply questions whether a solution can be found if L and w are not arbitrary.
  • It is mentioned that in real numbers, a linear combination of powers of e cannot equal -1, complicating the solution.
  • One participant suggests that setting L equal to w could simplify the problem, although this is described as trivial.
  • A later post requests a specific solution for w = 24 and L = 3500 while still seeking a general solution for any values of L and w.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the solvability of the equation, with differing views on the implications of arbitrary versus specific values for L and w. The discussion remains unresolved regarding the general solution.

Contextual Notes

The discussion highlights limitations in finding a solution due to the nature of the equation and the conditions under which it is examined, particularly regarding the use of real versus complex numbers.

SolStis
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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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