Math Snap

STEP 1

Assumptions1. The formula for the magnitude of an earthquake is given by $R=\log \left(\frac{}{_{0}}\right)$. The intensity of a zero-level earthquake, $_{0}$, is13. The intensity of the earthquake in question, $$, is $4 \times10^{4}$ times the intensity of a zero-level earthquake

STEP 2

First, we need to find the intensity of the earthquake in question. We can do this by multiplying the intensity of a zero-level earthquake by the given factor.
$$= I_{0} \times Factor$$

STEP 3

Now, plug in the given values for the intensity of a zero-level earthquake and the factor to calculate the intensity of the earthquake.
$$=1 \times \times10^{}$$

STEP 4

Calculate the intensity of the earthquake.
$$=1 \times4 \times10^{4} =4 \times10^{4}$$

STEP 5

Now that we have the intensity of the earthquake, we can find the magnitude of the earthquake using the given formula.
$$R=\log \left(\frac{}{_{0}}\right)$$

STEP 6

Plug in the values for the intensity of the earthquake and the intensity of a zero-level earthquake into the formula.
$$R=\log \left(\frac{4 \times10^{4}}{1}\right)$$

STEP 7

implify the fraction inside the logarithm.
$$R=\log \left(4 \times10^{4}\right)$$

Calculate the magnitude of the earthquake.
$$R=\log \left(4 \times10^{4}\right) \approx4.60$$The magnitude of an earthquake that is $4 \times10^{4}$ times as intense as a zero-level earthquake is approximately4.60.