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Real Life Scenario of Logarithm


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Real Life Application of Logarithms

Real life scenario of logarithms is on of the most crucial concept in our life. As we know, in our maths book of 9th-10th class, there is chapter named as LOGARITHM is very interesting chapter and its questions are some typical that is required technique to solve. Therefore, you must read this article “Real Life Application of Logarithms” carefully .

But, after solving these questions and getting knowledge of logarithm, Have you think that why you study this chapter what is use of LOGARITHM in our daily life. The LOGARITHM is used in the following application of the real life.

real life scenario of logarithms
real life scenario of logarithms

Real Life Application of Logarithm Earthquake Intensity Measurement

To know about the real life scenario of logarithms we start as an earthquake intensity measurement. For this, first we let to know some knowledge related to the earthquake measurement instrument known as Seismograph. which produces a graph output known as Seismograph.

real life scenario of logarithms
real life scenario of logarithms

 In the earthquake, a Seismic waves produces which travels through the Earth layer. The seismic wave gives out an energy that cause the earth to shake and also gives out low frequency acoustic energy.

Read More : 129 Maths Short Tricks

Now, this seismic waves is recorded by the seismograph instrument and its output is the seismographs graph. It is a record of the ground motion  in three co-ordinate axes (x, y, and z), with the z axis perpendicular to the Earth’s surface and the x- and y- axes parallel to the Earth’s surface. 

An earthquake’s hypo-center is the position where the strain energy stored in the rock is first released, marking the point where the fault begins to rupture. This occurs directly beneath the epicenter, at a distance known as the focal depth.

The amplitude of the seismic waves decreases with distance. Now, the instrument seismograph is based on a logarithmic scale, which is developed by Charles Richter in 1932 devised the first magnitude scale for measuring earthquake magnitude.

This is commonly known as the Richter scale. The magnitude of an earthquake is calculated by comparing the maximum amplitude of the signal with this reference event at a specific distance. 

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Real life scenario of logarithms

The Richter scale is a base-10 logarithmic scale, which defines magnitude as the logarithm of the ratio of the amplitude of the seismic waves to an arbitrary, minor amplitude. 


 where A is the amplitude of the earthquake recorded by the seismograph taken from 100 km (approx) from the epicenter of the earthquake and S is the standard earthquake whose amplitude is 1 micron approx. The magnitude of the standard earthquake is     M=logfrac{S}{S}=log1=0

 Since the Richter scale is a base-10 logarithmic scale, each number increase on the Richter scale indicates an intensity ten times stronger than the previous number on the scale.

Read : Why Log is not defined for negative base

For example: if we note the magnitude of the earthquake on the Richter scale as 2, then the other next magnitude on the scale is explained in the following table.

real life scenario of logarithms table

  Now according to the Richter scale magnitude of the earthquake, there is a lot of bad effect on our environments which may be a danger to the real world. Its details are given below in the table.

Richter MagnitudeDescriptionEarthquake Effects
0-2.0MicroNever Felt by People
2.0-2.9MinorFelt But Not Recorded
3.0-3.9MinorFelt But Not Damaged Cost
4.0-4.9LightCeiling Lights Swing But Not Damaged
5.0-5.9ModerateAffects weak construction and cause wall crack
6.0-6.9StrongAffects area up to 160 km from the epicenter
7.0-7.9MajorAffect area up to further area and cause several damaged
8.0-8.9GreatAffect area beyond 100 miles and cause severe damaged
9.0-9.9GreatAffect area beyond 1000 miles with disastrous effects
10+EpicNever Been Recorded

This is the one of the real life scenario of logarithms, which must be know.

Real Life Application of Logarithms in Determining pH Value

The Real Life scenario of Logarithms is to measure the acidic, basic or neutral of a substance that describe a chemical property in terms of pH value. To know this concept in details, click here.

Real Life Application of Logarithms in Measuring Sound Intensity

As we known that the sound carries energy and it is defined as I = P/A, where P is the power through which the energy E flows through per unit area A which is perpendicular to the direction of travel of the sound wave.

Now, according to physics rule, the sound intensity is measured in terms of loudness which is measured in terms of logarithm. Thus the sound intensity is defined as the \beta=(10dB)log\frac{I}{I_{0}}. In this definition, dB is the decibels. It is one-tenth of bel(B) and I and I0 are the sound intensity.

If I = I0, then \beta=(10dB)log\frac{I_{0}}{I_{0}}=(10dB)(log1)=0.

If I = 10I0, then \beta=(10dB)log\frac{10I_{0}}{I_{0}}=(10dB)(log1)=10dB etc. Hence, we can the different values.

Real Life Application of Logarithm in Calculating Complex Values

Sometimes we need to find the values of some complex calculations like x = (31)^(1/5) (5th root of 31), finding number of digits in the values of (12)^256 etc. To solve these types of problems, we need to use the logarithms.

The solving method of these problems will be learn in another maths blogs post. The URL of the post will be mentioned below in future.

Practice : Logarithm Questions Set 1

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