An earthquake was recorded which was 2,511,886 times more powerful than a reference level zero earthquake. What is the magnitude of this earthquake on the Richter scale? Intensity on the Richter scale is lo $\log \left( \frac { \mathrm { I } } { \mathrm { I } } \right)$
A) 5.4
B) 14.7
C) 6.4
D) 0.64

Question

Quizplus · Accepted Answer

The Richter scale is logarithmic, specifically base 10. The magnitude $M$ on the Richter scale for an earthquake of intensity $I$ relative to a reference intensity $I_0$ is given by $M = \log_{10} \left( \frac{I}{I_0} \right)$. Given $I/I_0 = 2,511,886$, we calculate $M = \log_{10}(2,511,886) \approx 6.4$.

An Earthquake Was Recorded Which Was 2,511,886 Times More Powerful log⁡(II)\log \left( \frac { \mathrm { I } } { \mathrm { I } } \right)log(II​)

An Earthquake Was Recorded Which Was 2,511,886 Times More Powerful $\log \left( \frac { \mathrm { I } } { \mathrm { I } } \right)$