Question

Please help me with this, I’ve been struggling with it for quite a while.

Answer 1

`E=10^(19.5961)` ergs

Explanation:

Given M = 5.2, we can substitute this into the formula and take Log formula into exponential form and solve henceforth.

First, log to exponential >>>>

`Log(x)=y\\Means\\10^y=x`

Let's put M = 5.2 into the formula and divide by 2/3 to get in log and then change it to exponential form:

`M=(2)/(3)Log((E)/(10^(11.8)))\\5.2=(2)/(3)Log((E)/(10^(11.8)))\\(5.2)/((2)/(3))=Log((E)/(10^(11.8)))\\7.7961=Log((E)/(10^(11.8)))\\10^(7.7961)=(E)/(10^(11.8))\\`

Now, we are looking for E, the Energy of the earthquake.

We need to cross multiply and find E. But remember rule of multiplying 2 same bases with different exponents. Its is shown below:

`10^(a)*10^(b)=10^(a+b)`

So we have:

`10^(7.7961)=(E)/(10^(11.8))\\10^(7.7961)*10^(11.8)=E\\10^(7.7961+11.8)=E\\E=10^(19.5961)`

So, Energy is 10^{19.5961} ergs