An exponential inequation is an inequality that involves exponential expressions. The inequality depends on the value of the base \( a \), which affects the direction of the inequality.
\[ a^{A(x)} > a^{B(x)} \]
This compares two exponential expressions with the same positive base.
\[ \begin{aligned} &\text{If } a > 1, \quad A(x) > B(x), \\ &\text{If } 0 < a < 1, \quad A(x) < B(x). \end{aligned} \]
When the base is greater than 1, the inequality direction is maintained. When the base is between 0 and 1, the inequality reverses.