상용로그

For the following exercises, find the value of the number shown on each logarithmic scale. Round all answers to the nearest thousandth.

Recall the formula for calculating the magnitude of an earthquake, $M=\frac{2}{3}\log \left(\frac{S}{{S}_{0}}\right).$ One earthquake has magnitude $3.9$ on the MMS scale. If a second earthquake has $750$ times as much energy as the first, find the magnitude of the second quake. Round to the nearest hundredth.

The formula for measuring sound intensity in decibels $D$ is defined by the equation $D=10\log \left(\frac{I}{{I}_{0}}\right),$ where $I$ is the intensity of the sound in watts per square meter and ${I}_{0}={10}^{-12}$ is the lowest level of sound that the average person can hear. How many decibels are emitted from a large orchestra with a sound intensity of $6.3\cdot {10}^{-3}$ watts per square meter?

The formula for measuring sound intensity in decibels $D$ is defined by the equation $D=10\log \left(\frac{I}{{I}_{0}}\right),$ where $I$ is the intensity of the sound in watts per square meter and ${I}_{0}={10}^{-12}$ is the lowest level of sound that the average person can hear. How many decibels are emitted from a rock concert with a sound intensity of $4.7\cdot {10}^{-1}$ watts per square meter?