Every student has studied and solved math problems related to log and antilog. We all were confronted with these problems, but how many of us ever questioned its purpose or what is its use in everyday life? In this article, we will explain some of the real life applications of log.

Before we get started with the practical utility, let’s first define, what exactly a log is?

Definition:

In mathematics, a log is defined as an operation that involves a number x, an exponent or power (n) and a base (b). This base must be raised or multiplied to produce that number x.

In other words, the number of times we need to multiply a number or base to get another particular value.

For example, how many times 3 is multiplied to have 27?

The answer is we need to multiply it three times: 3*3*3 = 27

Now, we can write it as Log3 (27) = 3 and say that log of 27 with base 3 is 3.

Practical Applications:

Logarithm is not just an operation or problem in mathematics, like some other math tools, it serves a very useful purpose in our lives.

Few of those utilities are given below:

For expressing very large numbers.

It can be used to measure the intensity of disasters like earthquakes.

Used for the measurement of acidity (pH value).

To measure the intensity of sound.

We will discuss all these fascinating utilities one by one, and try to prove that a logarithm is a lot more than just a math chapter.

1.Express large values:

Most often, while dealing with numbers, we face very large values like millions and billions. Here, with the use of log, we’re defining these big numbers in terms of their digits, i.e. the powers of 10 they got.

We can use this compressing property of log in defining a safety index. For instance, let’s assume that every year there are around 5500 casualties in the United States of America due to accidents. About 850 people die every year due to lung cancer.

Now, we will find the logarithm for all these statistics.

Log10 (5500) = 3.74

Log10 (850) = 2.92

Here, if one in x person dies as a result of any of the above cases each year, the safety index is simply the log of x. Higher the index, safer is the case study. In this way log assists in compressing those values that are very large in terms of magnitude.

2. Measuring Intensity of Earthquakes:

In earthquakes, seismic activity produces waves that tend to travel through the earth layer. When these waves reach the surface the transfer of energy causes the earth to shake. Now, these waves can be recorded on a seismograph.

A base 10 logarithm scale also called Richter scale is used to determine the magnitude. It does it by comparing the amplitude with the specific distance of the event.

Magnitude = M = log A/S

3. Measuring the sound Intensity:

According to the rules of physics, energy is carried by sound, which is expressed as Intensity = I = P/A. Here, P represents the power with which the energy flows through an area A, and the sound waves travels in a perpendicular direction to this area.

Intensity of sound is the degree of loudness, in terms of logarithm it can be computed as:

β = 10 decibel log I/I0

4. Measuring pH value:

The pH means power of hydrogen or potential of hydrogen ions in a solvent. The scale is a reference to know whether the substance is acidic or basic in nature. It ranges from 0 to 14, 7 is neutral pH that of water, above 7 is basic and below 7 is acidic.

We can use the log to measure the power of hydrogen ions of a substance as follows:

PH = -log10 [H+] here, we have to write the number of moles of the hydrogen of a particular substance.

In the end, I would like to state the fact that these are just a few examples of real life applications of log, and this math operation is far more useful in our daily lives. Math is a subject of concepts and constant practicing. If someone wants to learn math, he/she must learn the concepts in order to learn math. Similarly, practice is also very important for the learning of math.

In the above article, we’ve tried to evaluate a manual way of calculating different real world applications of math. In a manual way of calculating, the margin of error is minimum as if the formula goes wrong, one has to repeat the full process again in order to get the accurate results or solve the equations accurately.

If you are interested in calculating any log value in an easy and precise way, there are many online calculators available for this purpose like Log Calculator and for the inverse operation of log there are also Antilog Calculators available online. These online calculators are usually easy to use and provide accurate results. For these online calculators one has to find the best and free of cost calculator.

I am a researcher and a technical content writer. I have also been a math teacher since 2007. I like travelling, Love to explore new places, people & traditions.

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