An exponential function is defined as a function of the form:

\[ y = e^x \quad \text{with} \quad x : \forall x \in \mathbb{R}\]

Logarithmic equations are equations in which the unknown appears inside a logarithm. To solve them, it is crucial to understand the properties of logarithms and how these can be applied to isolate and determine the value of the unknown.

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 \(a^c = b\).

\[\log_a{b} = c \quad {\text{iff}} \quad a^c = b\]

An equation is a mathematical equality between two expressions containing one or more variables, called unknowns.