Why it matters

• Understand logs as the inverse of exponential functions.
• Use log rules to simplify expressions and solve quickly.
• Solve logarithmic equations and check domain restrictions.
• Use change of base to compute any logarithm on a calculator.
• Model “extreme” scales like pH, earthquakes, and sound intensity.
• Connect exponential growth/decay to real-world measurement systems.

Tip: Logs require positive arguments — always check inside the log.