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?
2026-03-27 05:36:37.1774589797
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Real life applications for logarithms
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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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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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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,
$$ (1+r)^N=\frac{c}{c-rP}$$
$$ (1+0.0015)^N=\frac{1000}{1000-0.0015. 100000}$$
$$ (1.0015)^N=\frac{1000}{1000-0.0015 .100000}\approx1.1764705882352941$$
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
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.