How to solve for a variable in an exponential equation

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Alice Faisal
Alice Faisal 2018-7-19
评论： Walter Roberson 2018-7-20
I want to solve this function for rs.. I used this code
syms ra rb rs Vr
Eq1 = Vr == exp((-pi*ra)/rs)+exp((-pi*rb)/rs);
t_sol = solve(Eq1, rs)
but I am getting an empty sym can anyone help me it's urgent

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回答（1 个）

Walter Roberson
Walter Roberson 2018-7-19
There is no closed form solution for that.
In Maple notation,
rs := -Pi * rb / RootOf(-exp(_Z)+Vr-exp(ra*_Z/rb))
Here, RootOf(-exp(_Z)+Vr-exp(ra*_Z/rb)) stands in for the set of values, _Z, such that the expression inside RootOf() becomes zero -- the roots of the equation. However, there is no closed form expression to derive that set.
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Alice Faisal
Alice Faisal 2018-7-19
Yes this is the correct answer, how did you get it using matlab? Because I need to try other vales for ra which is 2.30 and rb =6.89 Thank you so much in advance
Walter Roberson
Walter Roberson 2018-7-20
Assuming you mean 2.30E6 and 6.89E6 then 1.8887251678153105468716736113549*10^7
I used a different package, but I did the equivalent of using vpasolve() with an initial value of rs = 500000000

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