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Uses of Logarithms

Date: 07/20/2002 at 08:48:43
From: Nadine
Subject: Logarithms in daily life


I'd like to know how Logarithms and/or Log Inequalitiesare used on 
a daily basis, or in daily life.  What industries use them?  What for? 

Date: 07/20/2002 at 09:29:21
From: Doctor Tom
Subject: Re: Logarithms in the daily life

Hi Nadine,

It depends on what you mean by "daily life".  I have never,
for example, used logarithms to help balance my checkbook :^)

But any time you need to convert multiplications to additions,
they can be useful.  For example, if you get a loan at a
bank that has continuous interest (they all do), if you
need to calculate how long it will take to pay it back, you
need to use logarithms.

If you are a scientist studying anything with exponential
growth, like biologists studying populations, physicists
studying nuclear reactions, chemists studying chain
reactions; or a banker calculating how long it will take for
investments to reach certain levels at given interest rates,
you need to use logarithms.

If you are a physiologist looking at how the eye reacts to
light or the ear to sound, both are so-called "logarithmic
devices", i.e., if you double the light or the sound, the
reaction of the eye or ear is to signal not a double
strength, but rather an increase by a fixed step.  That
way you can see light or hear sound in a huge range without
having a complex signaling system.

Electrical engineers use logarithms to work on signal
decay.  Similarly with communications experts.  Computer
scientists looking at how fast programs run with respect
to the size of the inputs use logarithms often.  For
example, most good sorting programs take time proportional
to n*log(n) to sort a list of n items.

There are probably plenty more examples, but these should
get you started in thinking about this. 

- Doctor Tom, The Math Forum 
Associated Topics:
High School About Math
High School Logs

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