You are watching: Identify the base and the exponent

What I"m looking for is basically the opposite: provided the exponent, I want to find the equivalent base: therefore if the number is $n$ and the exponent is $k$, I"m trying to find a function that calculates a base $b$ so the $b^k = n$.

Does such a role exists? What is that name?

The most organic thing come say is come say the $b^k=c$ implies $b= c^1/k$, at least if $b$ and $c$ space positive. Girlfriend can call this the $k$th root, i.e. $b=sqrt

Otherwise $b^k = n$ implies $k log_c b = log_c n$, for this reason $b = c^(log_c n) / k$ for any sensible $c$ such as $e$ or $10$ or $2$

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utilizing integers $a$ and also $x$ in $a^x$, why walk the # of number of the exponentiated strength multiplied by the $log_10(a)$ same $pm1$ the exponent x?

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