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If we have the expression $a=x^{c\cdot x+1}$ where the values of $a,c$ are known, how can we find the value of $x$?

I tried using log but it yields: $x = a ^ {(1/x)/(c-1/x)}$ from which I can't find any solution.

Thanks.

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    The straightforward iteration $x' = a^{1/(cx+1)}$ seems to converge (and quickly) for all positive $a,c$ (I have not proved it).2011-10-14

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