Logarithms with integer bases

Let $n\>1$ be an integer. The function ${\log }_n\left(x\right)$, which is read the "logarithm (base $n$) of $x$" or the "base $n$ logarithm of $x$" is the inverse of the function $f\left(x\right)\=n^x$. Thus, $b\=n^a$ exactly when $a\={\log }_n\left(b\right)$. The domain of ${\log }_n\left(x\right)$ is the set of positive numbers. The range of ${\log }_n\left(x\right)$ is all numbers.

A logarithm is an exponent: ${\log }_n\left(b\right)$ is the power to which you raise $n$ to obtain the value $b$. Mathematically, $n^{{\log }_n\left(b\right)}\=b$.

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