E is measured in kWh hours.
If the average household uses 247 kWh hours per month,
how many months would the energy generated released by an earthquake measuring 7.7 on the richterscale power 4.8 million households.
Not sure where to start with this question apart from inputting 247kWh in place of E.
Any help is greatly appreciated.
Thank you
You don’t want to substitute $247$ for $E$: $E$ is the energy released by the earthquake, not the energy used by a household in a month. You want to use the Richter number to find $E$, then compute the total monthly energy consumption of $4.8$ million households, and finally see how many times that amount is released by the earthquake. I’ll get you started.
Substitute the Richter number $7.7$ for $M$ in your formula for the Richter number, and solve for $E$:
$$7.7=\frac23\log_{10}\frac{E}{0.007}\;,$$
so $$\log_{10}\frac{E}{0.007}=\frac32\cdot7.7=11.55\;.$$
Now exponentiate to get rid of the log:
$$\frac{E}{0.007}=10^{\log_{10}(E/0.007)}=10^{11.55}\;.$$
Multiply by $0.007$ to get $E$, the energy released in kWh:
$$E=0.007\cdot10^{11.55}\approx2.48\times10^9\text{ kWh}\;.$$
