A severe earthquake is many many times stronger than a shake of the table. How to measure both of them in a scale from 1 to 10? The sound of a bomb blast is many times highly intense than a whisper. How to measure them in a scale of 1 to 100 ?
Here logarithms comes to our help.
we know,
10^2 = 100
log 100 = 2.0000
(base 10)
2.0000 is the logarithm of 100 to the base of 10
similarly,
log 10000000000 = 10.0000
(base 10)
Hence using the idea of logarithm, we can represent any number lying between 100 and 10000 crores in the scale of 2 to 10.
example:
log 102456 = 5.010537
(base 10)
Long range of numbers can be compressed using logarithms.
In the case of earthquake, the formula is,
R = log (A/A0)
A0- the intensity of smallest detectable shock wave by seismograph.
A - the intensity of earthquake wave
If we get R as 3, the earthquake is 1000 times intense than the smallest disturbance. Since log 1000 = 3.0000 This scale is popularly known as Richter scale.
Formula for measuring sound intensity
d = log (P/P0)
P0 - weakest sound human can hear.
P - real intensity of sound.
Here the unit is decibel. D= 50 decibel means the sound is 10000 times stronger than a murmur.
Logarithms is originally invented to make numerical calculations easy. But the advent of electronic calculators and computers made it obsolete. But the logarithmic function is still useful as above.