The Richter scale is used to measure the intensity of an earthquake. If E, measured in joules, is the energy released during an earthquake, then the magnitude is given by,
M = 2/3 log(E/E_0)
Where E_0 = 10^4.4 joules
i. If 8 x 10^14 joules of energy are released during an earthquake, what is the magnitude of the earthquake?
ii. How much energy will be released in an earthquake with a magnitude of 5.9?
i. Since the amount of energy, E in this instance, is 8* 10^14, just plug 8*10^14 into (E/E_0). Then 8*10^14 / 10^4.4 would get you the right side of the equation. After that, calculating the magnitude would mean 2/3 log 31848573644.3(according to google calculator, but don't trust me on this one, I'd recommend you find some way to calculate it). solving 2/3 log 31848573644.3 you get 7.00205999133(I'd really recommend a calculator for this one).
ii. lol I can't solve it rn, since I'm on a car, but I'd imagine that you would do the reverse of #1, as you know that M is 5.9, and you already have E_0, so you can write the equation 2/3 log (E * 10^4.4) = 5.9, and from then on, you'd need some knowledge of logs and probably a calculator with u to solve it