The Richter magnitude of an earthquake, M, is related to the energy released in ergs, E, by the formula M=2/3log(E/10^11.8). Find the energy released by an earthquake of magnitude 4.2

Question

The Richter magnitude of an earthquake, M, is related to the energy released in ergs, E, by the formula M=2/3log(E/10^11.8).  Find the energy released by an earthquake of magnitude 4.2

mani_jha · Answer

Just substitute M=4.2 in the given equation. Make the whole log term the subject.
$$\log(E/10^{11.8})=3M/2$$
Then, remove the log,:
$$(E/10^{11.8})=10^{3M/2}$$
Then calculate E. Did you understand?

anonymous · Answer

Why can you remove the log? Im sorry im really new at these

anonymous · Answer

Oh sorry i get it! Thank you so much

mani_jha · Answer

What is the definition of logarithm? It is the power to which the base(in this case it is 10) must be raised so that it is equal to the number of whose logarithm is being taken.
Consider log 100=2(It is 2 because 10 multiplied by itself becomes 100)
So, coversely you can write 10^2=100