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Logarithms in Real Life Applications

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Joey Uy

on 18 March 2014

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Transcript of Logarithms in Real Life Applications

EARTHQUAKES
Magnitude of an earthquake is logarithmic
Used for predicting coming earthquakes
Richter Scale: base-10 logarithmic scale
CHEMISTRY
Solution's pH defined by
t= hydronium ion concentration in mol/liter
Round pH values to the nearest 10th
Radioactive decay
Used for geology
Half-life: time taken for the radioactivity of a specified isotope to fall to half its original value
Carbon dating
Radiometric dating technique
Estimates age of organic materials
Willard Libby
MEASURING SOUND
Standard unit: decibels
Decibel scale: reflection of the logarithmic response of the human ear to changes in sound intensity
Measured by first assigning an intensity I0 to a soft sound
Equation:
POPULATION GROWTH
Natural logarithms and exponential functions to determine increments of certain measurements
Measured to predict death rates, population increments, regional birth/death rates
Can be expanded into weeks, days, years, etc.
ECONOMICS
Make linear/exponential relationships
Analyzes the growth rate relationship of variables
Natural logarithm: grows at a constant percentage rate; log of variable will grow as a function of time
Finance: interest rates, stock prices, value of currency
BENFORD'S LAW
Frank Benford: American physicists
First-digit law
Frequency distribution of digits in numerous sources of data
Applicable in:
Street adresses
Stock prices
Death rates
Physical/mathematical constants
Logarithms in Real Life Applications
Joey Uy: The Preuss School UCSD
March 18, 2014; 1:05 P.M., EST

Equation
Logarithmic Scale
Full transcript