# No Closed Form Solution?

• Jul 5th 2012, 06:50 PM
visserthree
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:

Attachment 24233

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

Any help would be much appreciated!
• Jul 5th 2012, 07:43 PM
Soroban
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:

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

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

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

• Jul 6th 2012, 10:05 AM
Wilmer
Re: No Closed Form Solution?
Same problem with calculating i in most annuity formulas; like:
F = A[(1 + i)^n - 1] / i