# Thread: No Closed Form Solution?

1. ## 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:

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

Any help would be much appreciated!

2. ## Re: No Closed Form Solution?

Hello, visserthree!

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

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

Other examples are:

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

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

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

3. ## Re: No Closed Form Solution?

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