Question

What is the magnitude of an earthquake that is 5011 times more than a standard earthquake round the answer to the nearest 10th

Answer 1

Given:

Intensity of earthquake is 5011 times more than

To find:

The magnitude of an earthquake that is 5011 times more than a standard earthquake.

Solution:

The magnitude of an earthquake:

$M=\log \left(\frac{I_{1}}{I_{0}}\right)$

where $I_1$ is the measured intensity of earthquake and

$I_0$ is the standard intensity of earthquake

Given 5011 times more than a standard earthquake.

$I_{1}=5011 I_{0}$

Substitute this into the magnitude.

$M=\log \left(\frac{5011 I_{0}}{I_{0}}\right)$

Cancel both $I_0$ in the numerator and denominator.

$M=\log (5011)$

$M=3.6999$

M = 3.7

The magnitude of the earthquake is 3.7.