QuestionFind the earthquake magnitude using $R=\log \left(\frac{I}{1}\right)$ for $I=4 \times 10^{4}$ . Round to the nearest hundredth.

Studdy Solution

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.
$R=\log \left(4 \times10^{4}\right)$

STEP 8

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.

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QuestionFind the earthquake magnitude using $R=\log \left(\frac{I}{1}\right)$ for $I=4 \times 10^{4}$ . Round to the nearest hundredth.

Studdy Solution

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.
$R=\log \left(4 \times10^{4}\right)$

STEP 8

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.

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QuestionFind the earthquake magnitude using R=log⁡(I1)R=\log \left(\frac{I}{1}\right)R=log(1I​) for I=4×104I=4 \times 10^{4}I=4×104. Round to the nearest hundredth.

Studdy Solution

STEP 1

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.=I0×Factor = I_{0} \times Factor=I0​×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××10 =1 \times \times10^{}=1××10

STEP 4

Calculate the intensity of the earthquake.=1×4×104=4×104 =1 \times4 \times10^{4} =4 \times10^{4}=1×4×104=4×104

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⁡(0)R=\log \left(\frac{}{_{0}}\right)R=log(0​​)

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⁡(4×1041)R=\log \left(\frac{4 \times10^{4}}{1}\right)R=log(14×104​)

STEP 7

implify the fraction inside the logarithm.R=log⁡(4×104)R=\log \left(4 \times10^{4}\right)R=log(4×104)

STEP 8

Calculate the magnitude of the earthquake.R=log⁡(4×104)≈4.60R=\log \left(4 \times10^{4}\right) \approx4.60R=log(4×104)≈4.60The magnitude of an earthquake that is 4×1044 \times10^{4}4×104 times as intense as a zero-level earthquake is approximately4.60.

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QuestionFind the earthquake magnitude using $R=\log \left(\frac{I}{1}\right)$ for $I=4 \times 10^{4}$ . Round to the nearest hundredth.

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.
$= I_{0} \times Factor$

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

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

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

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

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.