REAL LIFE APPLICATION OF LOGARITHM
In our maths book of 9th-10th class, there is chapter named as LOGARITHM. It is very
interesting chapter and its questions are some typical that is required technique to solve. 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.
Earthquake Intensity Measurement
To know about the earthquake intensity measurement, first we let to know some
knowledge related to the earthquake measurement instrument known as Seismograph. which
produces a graph output known as Seismogram.
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. Now this seismic waves is recorded by the seismograph instrument and its
output is the seismogram 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 hypocenter 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.
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
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.
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.
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.