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What is the estimation for the positive root of the following equation $$ ax^k = (x+1)^{k-1} $$ where $a > 0$ (specifically $0 < a \leq 1$).

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Root estimation

What is the estimation for the positive root of the following equation $$ ax^k = (x+1)^{k-1} $$ where $a > 0$ (specifically $0 < a \leq 1$).