i need an example problem using log10E=11.4+1.5m
when E means radiated energy
and m is means magnitude. the log has a base of 10 that's why the 10 is there. please help!!!
Again, need an example problem relating it to earthquakes
To relate the equation log10E = 11.4 + 1.5m to earthquakes, we can use the equation to calculate the radiated energy (E) based on the magnitude (m) of an earthquake.
Let's say we want to find the radiated energy for an earthquake with a magnitude of 5.2. We can substitute m = 5.2 into the equation:
log10E = 11.4 + 1.5(5.2)
To solve this equation, we need to use logarithmic properties. We can first simplify the right side of the equation:
log10E = 11.4 + 7.8
Then, we combine the numbers on the right side:
log10E = 19.2
Now, to find the value of E, we need to undo the logarithm. We can rewrite the equation in exponential form:
10^(log10E) = 10^19.2
The logarithm and exponential function are inverse operations, so they cancel each other out:
E = 10^19.2
Using a calculator to evaluate 10^19.2, we find:
E ≈ 1.585 × 10^19
Therefore, the radiated energy (E) for an earthquake with a magnitude of 5.2 is approximately 1.585 × 10^19 units (the specific unit depends on the context of the equation).