In math, the logarithm of a number $n$ in base 10, finds the exponent where 10 has to be raised to, to produce $n$ again. So if $Log_{10}(n) = p$ then $10^p = n$.
What I'm looking for is essentially the opposite: given the exponent, I want to find the corresponding base: So if the number is $n$ and the exponent is $k$, I'm looking for a function that calculates a base $b$ so that $b^k = n$.
Does such a function exists? What is its name?
Best Answer
The most natural thing to say is to say that $b^k=c$ implies $b= c^{1/k}$, at least if $b$ and $c$ are positive. You can call this the $k$th root, i.e. $b=\sqrt[k]{c}$.
Otherwise $b^k = n$ implies $k \log_c b = \log_c n$, so $b = c^{(\log_c n) / k}$ for any sensible $c$ such as $e$ or $10$ or $2$