Charles Richter defined the magnitude of an earthquake to be ` M = log_(10) (I/S)`, where I is the intensity of the earthquake (measured by the amplitude of a seismograph reading taken 100 km from the epicentre of the earthquake) and S is the intensity of a ''standed earthquake'' (whose amplitude is 1 micron `=10^(-1)` cm).
Each number increase on the Richter scale indicates an intensity ten times stronger. For example. an earthquake of magnitude 5. An earthquake of magnitude 7 is 100 times stronger then an earthquake of magnitude 5. An earthquake of magnitude 8 is 1000 times stronger than an earthquake of magnitude 5.
The earthquake in city A registered `8.3` on the Richter scale. In the same year, another earthquake was recorded in city B that was four times stronger. What was the magnitude of the earthquake in city B ?

Answer

` 8.9020`

Explanation

`M _(A) = log_(10). (I_(A))/S`
`:. 8.3 = log_(10). (I_(A))/S`
Now `M_(B) = log_(10). (I_(B))/S`
Where ` I_(B) = 4I_(A)*`
` :. M_(B) = log_(10). (4I_(A))/S`
` = log_(10) 4+ log_(10). (I_(A))/S`
` = 0.6020 + 8.3`
` = 8.9020`
So, magnitude of earthquake in city B is ` 8.9020`.