In 2009, an earthquake of magnitude 6.7 shook the Kermadec Islands off the coast of New Zealand. Also in 2009, an earthquake of magnitude 5.1 occurred in the Alaska Peninsula. How many times stronger was the Kermadec earthquake than the Alaska earthquake? a)39.811

b)5.77

c)20.593

d)0.025

Given:

Magnitude m1= 6.7

Magnitude m2=5.1

Steps:

Let’s plug in these values into the formula

Log (I1/I2)= 6.7-5.1

Simplify the right side

log (I1/I2)=1.6

Now, change log equation to exponential equation using rule.

log a (x)=b could be written as x=a^b

Using this rule, we can rewrite the given equation and we know if there is no base given it means it has base as 10.

According to the rule, we can rewrite our equation

log (I1/I2)= 1.6 as I1/I2= 10^(1.6)

Simplify it

I1/I2= 39.811 approximately.

Solution:

Option A is correct. That’s 39.811 is correct.