# Logarithmic function Report

Can you think of a logarithmic function that you encounter in your work or in your personal life? I'm doing a report on this in school of how they can be helpful, and I really have no idea how they can be any use whatsoever. My teacher really didn't give us anything to go on.

Actually just a few examples would be good to give me an idea of what to write about. Thanks.

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Math Is Hard
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I live in California, and we pay great attention to the Richter scale out here!

vsage
Napier is usually given credit to inventing logarithms IIRC and I think most of the early use of logarithms outside colleges or whatever they were called back then was to make accounting easier. Newton's Law of Cooling is an equation that forensic scientists could use to determine the time of death of someone ideally. That's probably the easiest one I can give.

Edit: Living in Florida myself I would have been hard-pressed to remember the Richter Scale. Good one, Math Is Hard.

logarithms

since logarithmic function is the inverse of any exponential one, the logarithmic ones are for example in solutions of differential equations (in linear equations for example when you solve one with a series and then appears a logarithmic term for certain initial values), models to systems that are in our lifes, like population growth, thermodinamics of heat machines like air conditioner, models that describe heat radiation, nuclear decomposition, there are so many examples.

Math Is Hard
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As far as use in everyday life, how about the pH scale? I can't comment too much on this, but my understanding is that this is also logarithmic. vsage, you will know more about this, I bet!

vsage
Hah yeah I had thought about that one too but Newton's Law of Cooling holds a special place in my heart - most notably because I always forgot the dang thing at state Calculus competitions. pH, pOH and the decibels are all based on a logarithmic scale as well. Edit: One that you might see in ten or twenty years being used in everyday life is the term Qubit which is the quantum-computing equivalent to the bit but n Qubits can hold 2^n states (don't ask me why though I'm no physics major)

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Math Is Hard
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vsage said:
Hah yeah I had thought about that one too but Newton's Law of Cooling holds a special place in my heart - most notably because I always forgot the dang thing at state Calculus competitions.

State Calculus competitions?!? WOW! That's like so nerdy and so cool at the same time. I am trying to imaging what the cheerleaders are shouting at the competition at these events...hmmm..

2..4..6..8!