Question

The magnitude of an earthquake is measured on the Richter scale as a logarithm of the intensity of the shock wave. For magnitude Rand intensity, the formula is R = log/. Using this formulo, determine how many times more intense an earthquake that measures 7.5on the Richter scale is than an earthquake which measures 2.3 on the Richter scale. Round your answer to two decimal places,

Answer 1

To answer this question, first, we will compute the intensity of each earthquake.

Recall that:

$a=\log b\text{ if and only if }10^a=b.$

Therefore, using the given formula we get:

$I=10^R.$

Then, the intensity of an earthquake that measures 7.5 on the Richter scale is:

$I_{7.5}=10^{7.5},$

and the intensity of an earthquake which measures 2.3 on the Richter scale is:

$I_{2.3}=10^{2.3}.$

Now, notice that:

$\frac{I_{7.5}}{I_{2.3}}=\frac{10^{7.5}}{10^{2.3}}=10^{5.2}.$

We know that:

$10^{5.2}\approx158489.32.$

Answer:

$158489.32\text{ times more intense.}$