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Math Help - No Closed Form Solution?

  1. #1
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    No Closed Form Solution?

    Hi,

    I've been having problems solving equations where the variable I'm interested in appears inside and outside of powers. I'm not sure how to isolate the variable I want to find.

    I'm starting to think that there's no closed form solution to this and I may have to solve by other means. The question I'm trying to solve is as follows:

    No Closed Form Solution?-equation.png

    Re-arranging to find theta as a function of the other variables.

    Any help would be much appreciated!
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Re: No Closed Form Solution?

    Hello, visserthree!

    You are correct . . . There is no closed form.

    We see that \theta is "inside" an exponential function and "outside" of it.
    This is a transcendental function . . . which has no closed form.

    Other examples are:

    . . x + \sin x \:=\:1

    . . x + \ln x \:=\:1

    . . x + \arctan x \:=\:1

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  3. #3
    MHF Contributor
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    Re: No Closed Form Solution?

    Same problem with calculating i in most annuity formulas; like:
    F = A[(1 + i)^n - 1] / i
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