Final answer:
The magnitude of an earthquake is given by the equation M = log(I/I0), and we can solve for the magnitude of an earthquake that is 3 times as intense as in Japan by substituting the given values into the equation and solving for M.
Step-by-step explanation:
The magnitude of an earthquake is given by the equation M = log(I/I0), where I is the intensity of the earthquake and I0 is a reference intensity. In this case, the magnitude of the Japan earthquake is given as M = log(101). To find the magnitude of an earthquake that is 3 times as intense, we can set up the equation M = log(3I0) and solve for M.
First, we can simplify the equation M = log(3I0) by using the property of logarithms that states log(a*b) = log(a) + log(b). This gives us M = log(3) + log(I0). Since log(3) is a constant, we can rewrite the equation as M = k + log(I0), where k = log(3).
Next, we can substitute the value of M for the Japan earthquake, which is 7.2, and solve for k. This gives us 7.2 = k + log(101). Subtracting log(101) from both sides gives us k = 7.2 - log(101). Now we can substitute the value of k into the equation M = k + log(I0) and solve for the magnitude of the earthquake that is 3 times as intense as in Japan.
Overall, the magnitude of the earthquake that is 3 times as intense as in Japan is M = 7.2 - log(101) + log(I0).