Question

magnitude of an earthquake : $m = \log \frac{i}{s}$\
what is the magnitude of an earthquake that is 10,000 times more intense than a standard earthquake?\
$m = \square$

Explanation:

Step1: Define \( I \) and \( S \)

Let \( S \) be the intensity of a standard earthquake, so \( I = 10000S \) (since the earthquake is 10,000 times more intense).

Step2: Substitute into the formula

The magnitude formula is \( M=\log\frac{I}{S} \). Substitute \( I = 10000S \) into it:
\( M=\log\frac{10000S}{S} \)

Step3: Simplify the fraction

Simplify \( \frac{10000S}{S} \) (the \( S \) cancels out), we get \( 10000 \). So \( M = \log(10000) \)

Step4: Evaluate the logarithm

Since \( 10000 = 10^4 \), and \( \log(10^x)=x \) (for base 10 logarithm), so \( \log(10^4)=4 \)

Answer:

\( 4 \)