How can I transform exponential equation?
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I try to transform following exponential equation. I would like to obtain an analytical equation for x:
>> syms P A B x y z n
>> eqn1= P== A*((x+y)^n)+B*(x+z)
eqn1 =
P == A*(x + y)^n + B*(x + z)
>> solve (eqn1,x)
Warning: Unable to find explicit solution. For options, see
help.
> In solve (line 317)
ans =
Empty sym: 0-by-1
Any ideas why MATLAB can not solve above code?
回答（1 个）
John D'Errico
2017-10-15
编辑：John D'Errico
2017-10-15
0 个投票
Is there some reason why you think an analytical solution exists?
In fact, there is no analytical solution. Wanting magic to happen is not sufficient. How are your skills with a magic wand?
For example, suppose that n is greater than 4? There is a rather famous theorem showing that a polynomial equation of order greater than or equal to 5 has no analytical solution.
https://en.wikipedia.org/wiki/Abel–Ruffini_theorem
But in your case, n is completely unknown. n is a variable. So you have essentially a polynomial equation with non-constant coefficients, of completely unknown degree.
Only a crystal ball will suffice for you here.
2 个评论
Walter Roberson
2017-10-16
Yup. Let A = 1, B = 2, n = 5, y = 0, z = 1, P = 0, so 0 = 1*(x + 0)^5 + 2*(x+1), so x^5 + 2*x + 2 = 0 . There are no closed form solutions to that.
Konrad Dadej
2017-11-6
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