logarithmic function

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 \(a^c = b\).

Logarithmic inequalities are inequalities that involve one or more logarithmic expressions, in which the unknown \\(x\\9 appears either in the argument of the logarithm or, in some cases, in the base itself.

The exponential function \(y = a^x\) is a mathematical function in which a constant base \(a > 0\), \(a \neq 1\), is raised to the variable exponent \(x\). It describes exponential growth or decay and has domain \(\mathbb{R}\) and range \((0,\infty)\).

A logarithmic function is defined as a function of the form:

\[ y = \log{_a}x \quad \text{with} \quad a \gt 0 \quad a \neq 1 \quad \forall x \in \mathbb{R}^+\]