Question

richter defined the magnitude of an earthquake to be

$m = \log \frac { i } { s }$,

where $i$ is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and $s$ is the intensity of a \standard\ earthquake, which is barely detectable.

the magnitude of a standard earthquake is

$m = \log \frac { s } { s } = \square$

Explanation:

Step1: Simplify the fraction

Since \(I = S\) for a standard earthquake, we substitute \(I\) with \(S\) in the formula \(M=\log\frac{I}{S}\). So, \(\frac{I}{S}=\frac{S}{S} = 1\).

Step2: Calculate the logarithm

We know that the logarithm base - 10 of 1, i.e., \(\log_{10}1\). By the property of logarithms \(\log_{a}1 = 0\) for \(a>0,a
eq1\). Here \(a = 10\), so \(\log\frac{S}{S}=\log1=0\).

Answer:

\(0\)