Logarithmic Scale Visualizer – AP Precalculus

Learning Objectives

Understand why logarithmic scales compress wide-ranging data

Apply log₁₀ transformations to real-world measurements

Compare Richter, decibel, and pH scales

Calculate the actual magnitude difference between log scale values

Key Equations

\(\text{Richter: } M = \log_{10}(A/A_0)\)

\(\text{Decibel: } L = 10\log_{10}(I/I_0)\)

\(\text{pH: } -\log_{10}[H^+]\)

Why It Matters

Logarithmic scales make it possible to visualize data spanning many orders of magnitude. Each +1 on the Richter scale = 10× more amplitude (31.6× more energy). Each −1 on pH = 10× more acidic.