# 10 Common Applications Of Logarithms In Real-life

Mathematics is challenging yet fun. To understand mathematical concepts, one should be curious, open-minded, critical thinkers, and have knowledge of inductive and deductive reasoning in mathematics. Logarithms is a challenging mathematical concept, yet children find it easy to solve and apply due to its practicality.

Logarithms have been used for years and have reinforced various scientific discoveries over time. From early astronomical experiments to developing the first data storage device, concepts of exponents and logarithms are widely applied. Considering the same significance of the concept, in this article, we will cover some major real-life applications of logarithms.

Let’s get started!

## Understanding the concept of Logarithms

Logarithms is one of the oldest mathematical concepts that made various early scientific and mathematical discoveries possible. The history of logarithms dates back to the 17th century when a Scottish mathematician John Napier invented the concept of logarithms. He coined the term from the Greek words ‘logos’ and ‘arithmos’, which means ‘ratio’ and ‘number’.

Logarithms is a method to represent a significantly large mathematical value, and it helps to identify how many times a number has to be multiplied to get a desired other number. Logarithms are represented as a base number and power to that base number, using the equation logₕ a=y.

Let’s understand logarithms using an example.

Suppose you are a biologist interested in a rare species of bacteria. During your study, you noticed this rare form of bacteria’s population, which is 100, currently, increases at least ten times in an hour. You are interested in finding out how long it will take for the population to reach 10,000. Using logarithms, you can form the equation and find the required time.

logₕ a=y

Log₁₀ 100 = y

Here, ‘y’ will be the required time, ‘h’ is the rate of increment in population, and ‘a’ is the current population. The value of ‘y’ can be easily found with the help of the ‘log table’.

## Application of logarithms in real-life

Logarithms form a base of various scientific and mathematical procedures. Logarithms have wide practicality in solving calculus, statistics problems, calculating compound interest, measuring elasticity, performing astronomical calculations, assessing reaction rates, and whatnot. This article will cover some of the most common real-life applications of logarithms. The applications are-

### 1. Measuring the sound intensity

Sounds are measured using a scientific scale called the decibel scale, which works on the principle of logarithms. The scale can measure the faintest whispers and loudest of noises easily and accurately. Further, the decibel scale measures the different intensities of sounds by keeping the normal intensity of the sound as a reference point.

The sound above, below, and on the reference point are all accurately captured by the decibel scale. For instance, 5 times higher than normal intensity sound will be 5db on the decibel scale.

### 2. Stock market analysis

The ups and downs of the stock market require a lot of calculations and predictions, generally based on highly large values and calculations. The data obtained in the stock market are generally expressed in exponential form. Applying and understanding the exponential form of data in every situation is impossible.

Hence it is converted into logarithms for better understanding. Data transformation and normalization during stock market analysis are also carried out using the multiplicative properties of logarithms.

### 3. Studying the process of decay of radioactive elements

Another great application of logarithms in real life is studying the exponential decay process of radioactive elements. The decay of radioactive elements varies to a wide range, from a few seconds to decades. Examples of Exponential decay and growth both utilize the use of logarithms.

Logarithms help to study the half-life of radioactive elements and assess the decay rate and other processes related to radioactive elements, such as medical imaging.

Radiocarbon dating is the process of studying the age of geological and archaeological objects infused with radioactive carbon isotopes (C-14) in organic matter. This process helps to identify how old an object is and how long it could have been preserved without decaying and provides an insight into a human’s history timeline. Logarithms here help to convert complex exponential decay equations into simple linear equations for a better understanding of laymen and professionals.

### 5. Assessing the magnitude of earthquakes using the Richter scale

Richter scale is a scale widely used for assessing the magnitude of earthquakes by studying the disturbances in the plates of the earth’s layers. This scale works on the principle of logarithms. The energy released from the seismic waves is generally very high in intensity, requiring exponential equations to represent it.

Also, comparing the magnitude of two or more two earthquakes requires logarithms to solve the complex exponential equations. Logarithms simplify the representation and understanding of complex and large exponential values, resulting in better application of the obtained information.

### 6. Measuring pH levels of chemicals

Logarithms are widely applied in the process where studying pH level is important. pH levels help to identify the acidic and alkaline nature of the substances, such as soil, chemical elements, etc. pH levels can be studied through a pH scale that works based on the concept of logarithms.

The PH scale helps determine the concentration of hydrogen ions in the elements or substances and the application of Hydrogen ion-infused elements in various chemical and environmental processes.

### 7. Calculating the growth of the human species or other living species

Logarithms are also applied in the biological field for assessing and calculating the growth of human species and other living species, generally calculated in exponential form. Logarithms come in handy in studying the exponential growth of populations, the speed of doubling the population, comparing the growth rate of two populations predicting the future growth or decline rate of the population, and aiding in studies related to environment and biodiversity.

Studying human populations using logarithms helps in better planning and making policies for the welfare of the citizens, whereas studying bacteria or other living species populations is useful for understanding their life cycles and processes.

### 8. Data compression

Ever wondered how such large data obtained from various organizations and governments is stored and used? Storing such large data requires various storage devices, which will still be insufficient. In that case, the data compression technique is used, which uses logarithms to simplify and compress the data.

The data is compressed using different coding processes, such as arithmetic, transform, Huffman, Delta, entropy, Shannon-Fano, run-length encoding, etc., based on logarithm and its application.

### 9. Analyzing drug concentrations in medicines

Pharmacology and pharmacokinetics also have major applications of logarithms in identifying drug concentration in medicines and regulating the use of drugs. Logarithms are also used to study the change in the concentration of drugs in the human body over time.

Further, logarithms help to assess how long the drug will stay in the human body and when the effects will wear off. Whether the drug is distributed equally in the whole body or not is also studied through logarithms.

### 10. Sensation and perception

Another important area where logarithms are used is in the scientific study of sensation and perception using the highly renowned Weber’s and Steven’s power laws. Psychophysics and signal detection theory (SDT) also require the application of logarithms to estimate the presence or absence of stimulus and the intensity of the stimulus present. Identifying the magnitude of stimulus and sensory adaptation requires logarithmic scaling.

## Concluding thoughts

Logarithms is a highly used mathematical concept that makes the findings, representation, and interpretation of data from various disciplines easy and convenient. Understanding and applying logarithms in real life makes various complex processes easy to understand. Solving logarithmic equations is a discovery learning activity that helps discover and predict various phenomena.