Understand why logarithmic scales compress wide-ranging data
Apply logโโ 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 = 10ร more amplitude (31.6ร more energy). Each โ1 on pH = 10ร more acidic.
Tags
logarithmlog scaleRichterdecibelpHAP Precalculus
ModeEarthquake
Selectedโ
Scale Mode
Custom Value 5.0
Data Points
Comparison
Select two data points to compare their actual magnitude difference.
Quick Quiz
An earthquake of magnitude 7.0 releases how many times more energy than a 5.0 earthquake?