# Real life applications for logarithms [duplicate]

Can someone please tell me what purposes logarithms have in the everyday world? What non-theoretical applications are they in and when would one use them?

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## marked as duplicate by Ink, mau, naslundx, Najib Idrissi, Mark BennetApr 24 '14 at 9:27

Most of the answers to this question apply here. I'm tempted to close as a duplicate. – Rahul Apr 24 '14 at 7:10
Wow! This is probably a duplicate then... – Joao Apr 24 '14 at 7:12

The way in which our sense-organs $($eye, ear, etc.$)$ perceive the outside world $($light, sound, etc.$)$ is logarithmic; e.g., if a sound becomes $a^n$ times stronger, we only perceive it as n times stronger.

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Wow! That is really amazing! – Joao Apr 24 '14 at 7:07
What's $$a$$ for humans? – uoɥʇʎPʎzɐɹC Apr 15 at 12:00

Anywhere you find exponentials you will find logarithms. For example, if a population (people, animals, bacteria, whatever) is allowed to grow unchecked at a constant rate of reproduction, then the population at time $t$ will be $r^t$ times as large as the initial population. So the time required for the population to increase by a factor of $k$ is $\log_rk$.

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Logarithmic scales such as decibels for sound and the Richter scale for earthquakes.

When I was young, logarithms had an even more practical use: multiplying and dividing numbers.

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If you want to design a system to control/command something, a super popular method requires using some diagrams (Bode plots) where the property of logarithms of turning multiplication into addition is very useful.

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Some sea shells are quite perfect logarithmic spirals! :) In nature we have plenty of this!

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You can use it in mortgage calculation. If you have a limit value to pay monthly for your house mortgage and if you wonder how many months needs to pay , you need to use logarithm. (It gives you idea about your budget and payment time)

With a fixed rate mortgage (interest is r), the borrower agrees to pay off the loan P completely at the end of the loan's term, so the amount owed at month N must be zero. For this to happen, the monthly payment c can be obtained from the previous equation to obtain: \begin{align} c & {} = \frac{r}{1-(1+r)^{-N}}P \end{align}

$$(1+r)^N=\frac{c}{c-rP}$$

$$(1+r)^N=\frac{c}{c-rP}$$

For example :

You plan to get ${$}100,000$from bank and interest rate is$0.15$and you plan to pay each month$1,000 ,

in this case,

$$(1+r)^N=\frac{c}{c-rP}$$

$$(1+0.0015)^N=\frac{2000}{2000-0.0015. 100000}$$

$$(1.0015)^N=\frac{2000}{2000-0.0015 .100000}\approx1.1764705882352941$$

You need to calculate $N=\log_{1.0015}(1.1764705882352941)=\frac{\log(1.1764705882352941)}{\log (1.0015)}\approx \frac{0.07058107428570726667356900039616}{6.50953.10^{-4}}\approx108.42 months$

It gives you an idea about how many months you need to pay your mortgage payments with your payment budget. Please see Reference wiki page for detailed mortgage formulas

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