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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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    Solving this kind of equation usually requires the [Lambert W function](http://en.wikipedia.org/wiki/Lambert_W_function).2011-10-13
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    ...actually, after wrestling with this for a while, it doesn't look to me that this can be massaged into something where Lambert applies; you have an addition in the exponent, but none in the base. You may need to use Newton-Raphson for this...2011-10-14
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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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