QuestionWhat is the earthquake magnitude for intensity $I = 3 \times 10^{7}$ using $R=\log \left(\frac{I}{1}\right)$ ? Round to the nearest hundredth.

Studdy Solution

STEP 1

Assumptions1. The formula for the magnitude of an earthquake is $R=\log \left(\frac{}{_{0}}\right)$ . The intensity of a zero-level earthquake is $_{0}=1$
3. The intensity of the given earthquake is $3 \times10^{7}$ times the intensity of a zero-level earthquake

STEP 2

First, we need to find the intensity of the given earthquake. 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 given earthquake.
$=1 \times3 \times10^{7}$

STEP 4

Calculate the intensity of the given earthquake.
$=1 \times3 \times10^{7} =3 \times10^{7}$

STEP 5

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

STEP 6

Plug in the values for the intensity of the given earthquake and the intensity of a zero-level earthquake into the formula to calculate the magnitude of the earthquake.
$R=\log \left(\frac{3 \times10^{}}{1}\right)$

STEP 7

implify the fraction inside the logarithm.
$R=\log \left(3 \times10^{7}\right)$

STEP 8

Calculate the magnitude of the earthquake.
$R=\log \left(3 \times10^{7}\right) \approx7.48$ The magnitude of the earthquake that is $3 \times10^{7}$ times as intense as a zero-level earthquake is approximately7.48.

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QuestionWhat is the earthquake magnitude for intensity $I = 3 \times 10^{7}$ using $R=\log \left(\frac{I}{1}\right)$ ? Round to the nearest hundredth.

Studdy Solution

STEP 1

Assumptions1. The formula for the magnitude of an earthquake is $R=\log \left(\frac{}{_{0}}\right)$ . The intensity of a zero-level earthquake is $_{0}=1$
3. The intensity of the given earthquake is $3 \times10^{7}$ times the intensity of a zero-level earthquake

STEP 2

First, we need to find the intensity of the given earthquake. 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 given earthquake.
$=1 \times3 \times10^{7}$

STEP 4

Calculate the intensity of the given earthquake.
$=1 \times3 \times10^{7} =3 \times10^{7}$

STEP 5

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

STEP 6

Plug in the values for the intensity of the given earthquake and the intensity of a zero-level earthquake into the formula to calculate the magnitude of the earthquake.
$R=\log \left(\frac{3 \times10^{}}{1}\right)$

STEP 7

implify the fraction inside the logarithm.
$R=\log \left(3 \times10^{7}\right)$

STEP 8

Calculate the magnitude of the earthquake.
$R=\log \left(3 \times10^{7}\right) \approx7.48$ The magnitude of the earthquake that is $3 \times10^{7}$ times as intense as a zero-level earthquake is approximately7.48.

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QuestionWhat is the earthquake magnitude for intensity I=3×107I = 3 \times 10^{7}I=3×107 using R=log⁡(I1)R=\log \left(\frac{I}{1}\right)R=log(1I​)? Round to the nearest hundredth.

Studdy Solution

STEP 1

STEP 2

First, we need to find the intensity of the given earthquake. 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 given earthquake.=1×3×107 =1 \times3 \times10^{7}=1×3×107

STEP 4

Calculate the intensity of the given earthquake.=1×3×107=3×107 =1 \times3 \times10^{7} =3 \times10^{7}=1×3×107=3×107

STEP 5

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

STEP 6

Plug in the values for the intensity of the given earthquake and the intensity of a zero-level earthquake into the formula to calculate the magnitude of the earthquake.R=log⁡(3×101)R=\log \left(\frac{3 \times10^{}}{1}\right)R=log(13×10​)

STEP 7

implify the fraction inside the logarithm.R=log⁡(3×107)R=\log \left(3 \times10^{7}\right)R=log(3×107)

STEP 8

Calculate the magnitude of the earthquake.R=log⁡(3×107)≈7.48R=\log \left(3 \times10^{7}\right) \approx7.48R=log(3×107)≈7.48The magnitude of the earthquake that is 3×1073 \times10^{7}3×107 times as intense as a zero-level earthquake is approximately7.48.

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QuestionWhat is the earthquake magnitude for intensity $I = 3 \times 10^{7}$ using $R=\log \left(\frac{I}{1}\right)$ ? Round to the nearest hundredth.

First, we need to find the intensity of the given earthquake. 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 given earthquake.
$=1 \times3 \times10^{7}$

Calculate the intensity of the given earthquake.
$=1 \times3 \times10^{7} =3 \times10^{7}$

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

Plug in the values for the intensity of the given earthquake and the intensity of a zero-level earthquake into the formula to calculate the magnitude of the earthquake.
$R=\log \left(\frac{3 \times10^{}}{1}\right)$

implify the fraction inside the logarithm.
$R=\log \left(3 \times10^{7}\right)$

Calculate the magnitude of the earthquake.
$R=\log \left(3 \times10^{7}\right) \approx7.48$ The magnitude of the earthquake that is $3 \times10^{7}$ times as intense as a zero-level earthquake is approximately7.48.