  The logarithm function and the exponential function are, by nature, base
dependent. Thus, in this paper I introduces an arbitrary base in the logarithm
and exponential functions, both dependent on $q$, in order to have
$\log_a(x;q)$ and $a_q^x$. Some of the properties of these functions had been
analyzed. The logarithm function was applied to the entropy which resulted in
the $S_q = k[1 - \sum_{i = 1}^Wp_i^{q}]/[1 - e^{1 - q}]$ expression.
