Department of Mathematics --- College of Science --- University of Utah

Mathematics 1010 online

Applications using Logarithmic Equations

Using Logarithmic equations to solve problems

Example #1 (Sound Intensity): The relationship between the number of decibels B and the intensity of a sound I in watts per centimeter squared is given by:


Determine the intensity of a sound I if it registers 125 decibels on a decibel meter.


In examples #2 and 3, compare the intensities of the two earthquakes.


Location Date Magnitude
San Francisco, CA 4/18/1906 8.3
Napa, CA 9/3/2000 4.9

Formula: R = log10I, where I is the intensity of the shockwave and R is the magnitude of an earthquake.



Location Date Magnitude
El Salvador 2/13/2001 6.5
Columbia 1/25/1999 5.7

Example #4 (Human Memory Model): The average score A for a group of students who took a test t months after the completion of a course is given by the human memory model:
A = 80 - log10(t + 1)12

How long after completing the course will the average score fall to A = 72?


Example #5 (Newton's Law of Cooling): You place a tray of water at 60oF in a freezer that is set at 60°F. The water cools according to Newton's Law of Cooling:


a) The water freezes in 4 hours. What is the constant k? (Hint: Water freezes at 32°F.)


b) You lower the temperature in the freezer to -10°F. At this temperature, how long will it take for the ice cubes to form?


c) The initial temperature of the water is 50°F. The freezer temperature is 0°F. How long will it take for the ice cubes to form?