^{x}= 12.

Now, I know that x is on (2,3), but that's about it.

I know that usually you would take log

_{x}of both sides which would isolate the exponent, or even take the x

^{th}root of both sides to isolate the base.

I've tried both methods, but nothing seems to work. Whenever I do anything with logs and radicals, I end up with ln(x

^{x}) = ln(12), which just takes me back to the original equation.

Can anyone shed some light on this for me?

In case you're wondering where I got this, I was looking at nominal interest rates compounded n times per year.

Essentially, you would have FV = (1 +

^{i(n)}/

_{n})

^{n}

If you tried to solve for n (without a calculator) you would have a similar problem (as far as i can tell) [[see spoiler]]

**Spoiler:**

Also, I started thinking that you could use linear approximation for this. Can anyone confirm/deny that?

Thanks for your help!