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Name: Tanya D.
Status: student	
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Question:
I am investigating the importance of logarithms, in today's world. After surfing for hours on the web, all I found was that logs play a vital role in finance and astronomy. I could not find any further details. What I would like to know is how help in finance and astronomy.



Replies:
Logarithms can play a role anywhere you will find exponentials. In my field of engineering, an exponent can make it difficult to find some correlations to events, but a logarithm can linearize the equation to make it more manageable to solve. Also, graphically, log-log graphs can be easier to read and "see" the correlation between events. Where exponents exists in an equations, logarithms could be used in solving for certain variables related to the exponents. For example in biology, the growth of bacteria can be measure with the equation y(new)=y(old)*e^xt, where y(new) is the count of bacteria, y(old) is the previous amount of bacteria, x is a variable dependent on the bacteria strain, and t in the time of growth. In order to find t, one would have to use logarithms to solve for t. Although outdated because of advances in computers and calculators, logarithms are what make slide rules work. They allowed the linear addition (or subtraction) of logarithm which in turn is multiplication (and division) of numbers. If you happen to find an old slide rule, I suggest you learn how to use it by getting a slide rule manual at your local library. It gives you a good idea of how and why logarithms work. Also, you might look into the history of it a little more by looking for information on Napier. Good luck.

Chris Murphy, PE


Tanya,

Logarithms are useful in at least two major circumstances:

One is where exponential functions are used. Just as division is the inverse of multiplication, a logarithm is the inverse of an exponential function. In physics, a common use is radioactive decay. The amount of radioactive material remaining after some time passes is the product of the initial amount and an exponential function of (-t/t0). To calculate the amount remaining as a function of time requires an exponential function. To go backwards, to calculate the time passed as a function of the amount of radioactive material remaining, requires a logarithmic function.

Another is where the area under a 1/x curve is needed. When you learn calculus, you will see that the area under a 1/x curve is a ln(x). Anytime something changes at a rate proportional to 1/x, the total value is logarithmic. Such effects occur in electricity and magnetism. You may not see it until you study physics at the level of calculus (i.e. rates that are not constant), but logarithms are used.

Dr. Ken Mellendorf
Physics Instructor
Illinois Central College


First, a definition of logarithms: The "log(N)" to the base "a" is the power "p" to which "a" must be raised to obtain "N". So: a^p = N or a^(log(N)) = N. For example, 100 = 10^2 so the log of 100 to the base 10 is 2. Or in a less familiar example: 243 = 3^5. So 5 is the log(243) to the base 3.

Second, your specific inquiry would fill volumes so rather than just give you a list, I suggest you what I did and do a search on: www.google.com on the term: "logarithm applications". You will find dozens and dozens of sites that discuss various uses and applications of logarithms.

Vince Calder



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