Question

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

Answer 1

Answer:

$E=10^{19.5961}$ ergs

Step-by-step 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:

$M=\frac{2}{3}Log(\frac{E}{10^{11.8}})\\5.2=\frac{2}{3}Log(\frac{E}{10^{11.8}})\\\frac{5.2}{\frac{2}{3}}=Log(\frac{E}{10^{11.8}})\\7.7961=Log(\frac{E}{10^{11.8}})\\10^{7.7961}=\frac{E}{10^{11.8}}$

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:

$10^{7.7961}=\frac{E}{10^{11.8}}\\10^{7.7961}*10^{11.8}=E\\10^{7.7961+11.8}=E\\E=10^{19.5961}$

So, Energy is 10^{19.5961} ergs