Logarithms

Andy Grogan-Kaylor

2025-04-08

Definition

\[\color{purple}{y} = \color{red}{b}^\color{blue}{x}\]

\[\iff\]

\[\color{blue}{x} = \log_\color{red}{b}(\color{purple}{y})\]

Key Idea

The exponential and logarithmic functions are inverses of each other.

Exponential and Logarithmic Functions Are Mirror Images

Applications of Exponential and Logarithmic Functions

• Radioactive decay
• Disease spread
• Population growth