I am facing the following equation and I do not have any idea about how to solve it. $\dfrac{(n^c-1)^a}{n^{ac}}$ = $\dfrac{1}{2}$. I am free to choose $c$ (any constant). $a$ on the other hand can be any polynomial. I am not sure of what tags I should put here. Any editing will be appreciated.
2026-04-29 11:04:05.1777460645
N-th roots equation
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I'm assuming you want to express $n$ in terms of $a,c$. Take $a$th roots to get $$ 1 - n^{-c} = \frac{n^c-1}{n^c} = 2^{-1/a}. $$ Therefore $n^{-c} = 1-2^{-1/a}$, and so $n = (1-2^{-1/a})^{-1/c}$.