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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:

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

EARTHQUAKES

  • Magnitude of an earthquake is logarithmic
  • Used for predicting coming earthquakes
  • Richter Scale: base-10 logarithmic scale

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

Logarithmic Scale

Equation

Logarithms in Real Life Applications

Joey Uy: The Preuss School UCSD

March 18, 2014; 1:05 P.M., EST

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