Now, I know that x is on (2,3), but that's about it.
I know that usually you would take logx of both sides which would isolate the exponent, or even take the xth 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(xx) = 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]]
Then, 1000 = (1 + 0.1/n)n
(1000)1/n = 1 + 0.1/n
1000n = n / (n + 0.1)
And from there, I seem to keep going in circles.
1000n (n + 0.1) = n
1000n (1 + 0.1/n) = 1
1 + 0.1/n = 1000-n
1000 = (1 + 0.1/n)n
Also, I started thinking that you could use linear approximation for this. Can anyone confirm/deny that?
Thanks for your help!