Radicals emerge from the problem of solving equations of the form x^{n} = a, where n \in \mathbb{N}, n \geq 2, and a \in \mathbb{R}.

If a and b are positive real numbers, where a \neq 1, the logarithm of b to the base a, denoted as log{a} ⁡ ( b ), is defined as the real number c such that a^{c} = b.