Refresher - Logarithms

Earthquakes: In 1935 Charles Richter defined the magnitude of an earthquake to be $M={\log }_{}\frac{I}{S}$ where I is the intensity of the earthquake and S is the intensity of a ''standard earthquake.'' The Richter magnitudes are based on a logarithmic scale, base 10. What this means is that for each whole number you go up on the Richter scale, the intensity of the ground motion recorded by a seismograph is ten times stronger. Using this scale, a magnitude 6.0 earthquake would be ten times stronger than a magnitude 5.0 earthquake. A magnitude 8.0 earthquake would be (10x10) 100 times stronger than a magnitude 6.0 earthquake.

 

 

 

 

Acidity or Alkalinity: pH is a measure of how acidic or alkaline a substance is. The initials pH stand for "Potential of Hydrogen." The pH scale ranges from 0 to 14. Acids have pH values under 7, and alkalis have pH values over 7. pH equals the negative log of the concentration of H+ or stated as an equation, pH = -log[H+]. Therefore, when the concentration of H+ ions in a solution is 10^-14, the pH is 14. In pure water, the average concentration of H+ ions is 10^-7, the pH is 7. Because the pH scale is logarithmic, a difference of one pH unit represents a tenfold, or ten times change. For example, the acidity of lemon juice with a pH of 2 is ten times greater than that of vinegar with a pH of 3. A difference of 2 units, from 4 to 2, would mean that the acidity is one hundred times greater, and so on.

 

 

 

Math 1A/1B: Pre-Calculus by Dr. Sarah Eichorn and Dr. Rachel Lehman is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License Links to an external site..