If an earthquake has an intensity of I, then its magnitude, as computed by the Richter Scale, is given by $\mathrm { R } = \log \left( \frac { \mathrm { I } } { \mathrm { I } _ { 0 } } \right)$, where $\mathrm { I } _ { 0 }$ is the intensity of a small, measurable earthquake. (Consider $\mathrm { I } _ { 0 } = 1$ for this question.) If one earthquake has a magnitude of $3.0$ on the Richter scale and a second earthquake has a magnitude of $8.5$ on the Richter scale, how many times more intense (to the nearest whole number) is the second earthquake than the first?
A) 316,228
B) 316,227,766,017
C) 681
D) 2

Question

Quizplus · Accepted Answer

The intensity ratio between two earthquakes on the Richter scale is given by $10^{R_2 - R_1}$, where $R_2$ and $R_1$ are their respective magnitudes. For the given magnitudes of 8.5 and 3.0, the intensity ratio is $10^{8.5 - 3.0} = 10^{5.5} \approx 316,228$.

If an Earthquake Has an Intensity of I, Then Its R=log⁡(II0)\mathrm { R } = \log \left( \frac { \mathrm { I } } { \mathrm { I } _ { 0 } } \right)R=log(I0​I​)

If an Earthquake Has an Intensity of I, Then Its $\mathrm { R } = \log \left( \frac { \mathrm { I } } { \mathrm { I } _ { 0 } } \right)$