Question17. The magnitude, $M$, of an earthquake is measured using the Richter scale: $$M=\log \left(\frac{I}{I_{0}}\right)$$
A "great" earthquake measures about 8 on the Richter scale, while a "light" earthquake measures about 4. Does this mean that a great earthquake is twice as intense as a light earthquake? If so, explain why, and if not, explain why not, using mathematical reasoning.

Studdy Solution
Compare the intensities by finding the ratio of the intensity of a "great" earthquake to a "light" earthquake:
$$\text{Intensity Ratio} = \frac{I_{\text{great}}}{I_{\text{light}}} = \frac{I_0 \times 10^8}{I_0 \times 10^4} = 10^{8-4} = 10^4$$
This shows that a "great" earthquake is $10^4 = 10,000$ times more intense than a "light" earthquake, not twice as intense.
The conclusion is that a "great" earthquake is not twice as intense as a "light" earthquake; it is actually 10,000 times more intense due to the logarithmic nature of the Richter scale.