Question

An earthquake registers a 5.6 on the Richter scale. If the reference intensity of this quake was 7.3 × 109, what was the intensity of the earthquake?

Answer 1

log(x/7300000000) = 5.6 so

x/7300000000 = 10^5.8 = 398107.17

x = 2.9061823 x 10^15

Answer 2

`2.91* 10^(15)`

Explanation:

Since, an earthquake has a Richter scale magnitude,

`M=log((I)/(I_0))`

Where, I is the intensity of the earthquake,

While,
`I_0` is the reference intensity,

Given, M = 5.6,

And,
`I_0=7.3 * 10^9`

`\implies 5.6 = log((I)/(7.3 * 10^9))`

`5.6=log I - log(7.3* 10^9)` ( Because, log (a/b) = log a - log b ),

`5.6 = log I - 9.86332286012`

`log I = 15.4633228601`

`\implies I=10^(15.4633228601)=2.9061823449* 10^(15)\approx 2.91* 10^(15)`

Hence, the intensity of the earthquake is
`2.91* 10^(15)`.