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

Answer:

$2.91\times 10^{15}$

Step-by-step explanation:

Since, an earthquake has a Richter scale magnitude,

$M=log(\frac{I}{I_0})$

Where, I is the intensity of the earthquake,

While, $I_0$ is the reference intensity,

Given, M = 5.6,

And, $I_0=7.3 \times 10^9$

$\implies 5.6 = log(\frac{I}{7.3 \times 10^9})$

$5.6=log I - log(7.3\times 10^9)$    ( Because, log (a/b) = log a - log b ),

$5.6 = log I - 9.86332286012$

$log I = 15.4633228601$

$\implies I=10^{15.4633228601}=2.9061823449\times 10^{15}\approx 2.91\times 10^{15}$

Hence, the intensity of the earthquake is $2.91\times 10^{15}$.