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The Richter scale converts seismographic readings into numbers for measuring the magnitude of an earthquake according to this
function $$M ( x ) = \log \left( \frac { x } { x _ { 0 } } \right) , \text { where } x _ { 0 } = 10 ^ { - 3 } .$$
-What is the magnitude of an earthquake whose seismographic reading is 6.6 millimeters at a distance of 100 kilometers from its epicenter? Round the answer to the nearest tenth.
A) 2.8
B) 3.8
C) 2.5
D) 819.5

Question

Quizplus · Accepted Answer

The magnitude $M(x)$ of the earthquake is calculated using the given function $M(x) = \log\left(\frac{x}{x_0}\right)$, where $x = 6.6$ millimeters (or $6.6 \times 10^{-3}$ meters) and $x_0 = 10^{-3}$. Substituting these values into the formula gives $M(6.6) = \log\left(\frac{6.6 \times 10^{-3}}{10^{-3}}\right) = \log(6.6) \approx 3.8$.

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