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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 7.6 millimeters at a distance of 100 kilometers from its epicenter?
A) 0.38808
B) 0.20281
C) 3.8808
D) 2.0281

Question

Quizplus · Accepted Answer

The magnitude $M(x)$ of the earthquake can be calculated using the given formula and the value $x = 7.6$ millimeters (or $7.6 \times 10^{-3}$ meters). Plugging the values into the formula gives $M(7.6 \times 10^{-3}) = \log\left(\frac{7.6 \times 10^{-3}}{10^{-3}}\right) = \log(7.6) \approx 3.8808$.

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