Logarithmic Inequalities
Big Idea: Logarithmic inequalities involve finding the range of values of a variable that satisfy an inequality containing logarithmic expressions. The key challenge is understanding when the inequality sign flips based on the base of the logarithm.
📌 Prerequisites: Recall the Basics
Before diving in, remember these essential logarithm facts:
- $\log_a(x)$ is defined only when $x > 0$ and $a > 0$, $a \neq 1$
- $\log_a(x) = y \iff a^y = x$
- If $a > 1$, then $\log_a$ is an increasing function
- If $0 < a < 1$, then $\log_a$ is a decreasing function