Jun 16, 2020

Logarithms are an intricate part of mathematics.

This seemingly abstract topic is not limited to the realms of your textbook or inside your classroom. It does have many applications beyond your class.

Let’s get to that without further ado.

Logarithms are used for measuring the **magnitude of earthquakes.**

Logarithms are used for measuring the noise levels in **dBs (decibels)**.

They are used to measure the **pH level** of chemicals.

\(pH=log_{10}[H^+]\)

Logarithms are used in **radioactivity**, mainly to detect the **half life** of a radioactive element.

\(t_{1/2}= \frac{ln(2)} {λ} = \tau ln (2)\) [ln (2) = 0.693 ]

\(\lambda\) = decay constant,

\(t_{1/2}\) = half life of decaying quantity.

Logarithms are used to measure **exponential growth** or **exponential decay**. The best examples of these can be:

- The growth of money at a fixed rate of interest,

Say for example, you have $10,000 in your bank account at an interest of 2%. With the help of logarithms you’ll be able to know when your money’s going to reach $12,000.

- The growth of bacteria on a Petri dish,

If you have a petri dish having bacteria taking up around 0.1% space of the dish and you also know the fact that they divide every 30 minutes, you’ll be able to calculate the time by which the bacteria will fill up that entire dish through the use of logarithms.

Logarithms are used to measure **radioactive decay** is **radiocarbon dating**. Radiocarbon dating is the method of determining the age of an organic object by implementing the properties of radiocarbon (**Carbon- 14, \(^{14}C\)**).

Logarithms are used in specific calculations where **multiplications are turned into additions**.

Logarithms are also implemented to calculate the **exponential growth of population**.

Logarithmic calculations also arise in **calculus**. Such calculations are used for several calculations in the real world.

For e.g.: ∫(1/x) dx= log x + c

Logarithms are used in **combinatorics** problems. Combinatorics is a specific branch of mathematics that’s concerned with the study of finite discrete structures. But how are logarithms used here? Suppose you have to store a specific piece of data having “x” possible values. Then you’ll need “**log x**” bits for storing the data.

To sum up, we would say, logarithms are used mostly in almost all applications where a concept of exponentials come up for calculations.

If you come across anything like \(x= e^y\), you’ll have to implement logarithms in your calculations.

Logarithms are hugely used in statistics.

Logarithms are hugely applied in science and technology. The examples of their applications can be algorithm complexity analysis, binary tree, Dijkstra's algorithm that’s used to depict the shortest path between two points and so on.

Logarithms can turn multiplications into additions. This is immensely beneficial in humongous multiplication problems.

Logarithms can turn powers into multiplications.

Logarithms may seem pretty abstract from the hindsight but they do have huge importance in technology, geology, census, banking and many other relevant careers of life. So, don’t ignore logarithms and practice them to the best of your abilities.

That should be all for now. Hope you had a good read.

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Article Posted in: Information and Examples