Logarithms in the Real World

Logs in the Real World How do you use logarithms in the real world? Like most things that we are taught in math, most people would not be able to answer this question. Though many people have no clue how to use a logarithm in the real world or have ever needed to use one, there are still many uses for logs that are actually quite common. Three common uses for logs in the real world are calculating compound interest, calculating population growth or decay, and carbon dating. Using logs is a key component when solving for compound interest. Whenever you are calculating the interest on an investment that is compounded continuously, a natural exponential function is used. To solve for continuously compounded interest you use the formula A(t) = Pert, where P is the principal, r is the interest rate, and t is the number of years since the investment was made. Without the use of logs finding the interest on a continuously compounded investment would not be possible. Another use of logs in the real world is modeling data that increases or decreases over time. An example of this is calculating population growth. Population growth can be found using the formula P(t) = P(0)ekt , where k is the constant relative growth rate, and P(0) is the initial population, measure at time zero. Finding the constant growth or decay of any group of data would be much harder without use of logs. Carbon dating is a technique used by scientists to date fossils. It relies on the fact that the C14 isotope of carbon decays into another isotope of carbon, C12 at a rate proportional to its mass. This means that it has a constant rate of decay. The same equation is used for this as for continuous compounding and population growth. Though logarithms are not a part of most people daily lives it is a crucial mathematical expression in others. For some people there jobs would not be possible without the use of logs.

Works Cited:

Cited: http://betterexplained.com/articles/using-logs-in-the-real-world/ http://www.uiowa.edu/~examserv/mathmatters/tutorial_quiz/log_exp/realworldappslogarithm.html http://m.everythingmaths.co.za/grade-12/02-logarithms/02-logarithms-12.cnxmlplus