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Richter Magnitude Scale: A Logarithmic Scale for Earthquakes
See how logarithms turn huge swings in earthquake intensity into a simple number scale, with the Richter scale formula and step-by-step examples.
What You'll Learn
The Richter scale is a logarithmic scale, so each whole-number increase in magnitude means ten times more ground motion.
The formula is M equals log base 10 of I over I sub 0, comparing measured intensity to a reference intensity.
Because the scale is logarithmic, energy released grows even faster than intensity, roughly thirty-one times more energy per magnitude unit.
Comparing two earthquakes on the Richter scale is really just subtracting logarithms and rewriting the result as a power of ten.
Understanding logarithm rules makes it possible to convert between magnitude and intensity in both directions.
What You'll Practice
1
Comparing intensity ratios between two earthquakes with given Richter readings
2
Finding Richter scale readings when given intensity multipliers
3
Simplifying exponential expressions with subtraction of exponents
4
Solving logarithmic equations to determine earthquake magnitudes
Why This Matters
Understanding the Richter scale shows you how logarithms make extremely large numbers manageable in real-world science. This skill applies to measuring sound intensity (decibels), pH levels in chemistry, and any field where exponential scales compress vast ranges of data into readable measurements.
Before You Start — Make Sure You Can:
This Unit Includes
2 Video lessons
Practice exercises
Learning resources
Skills
Logarithms
Richter Scale
Exponential Functions
Exponent Rules
Logarithmic Scale
Real-World Applications
Ratios
ON Curriculum Aligned