How can I solve for n for something of this form?
(1.14)^(1/n) - 1 = 0.13/n
I managed to arrive at this:
n[(1.14)^(1/n) -1] = 0.13
But I don't know where to go from there.
I don't know a way to solve this equation algebraically.
I would use Newton's method to get an approximate value for n:
$\displaystyle f(n)=n\left((1.14)^{\frac1n}-1\right)-0.13~,~n\in \mathbb{R}$
Solve $\displaystyle f(n)=0$ for n.
I got $\displaystyle n \approx -8.3045$