Question

I have to find the values of A and B from the equation M=AlogE+B. M =magnitude and E =energy. There are two earthquakes where one the magnitude is 8.6, energy is 10^16. The other one is magnitude of 3.8, energy of 10^11. I am confused on how to solve two variables with two different magnitudes and energies on the one equation. So far i think i need to do simultanous equation working out but i don't know how.

Answer 1

since E had a value and not one of the unknown, the resulting equations to solve A and B is of linear... plugging in the given values for M and E, we'll have the following equations:
\[8.6=A \log {10^{16}}+B=16A+B~~~~~(1)\]
\[3.8=A \log {10^{11}}+B=11A+B~~~~~(2)\]
... that is... two equations (1) and (2), two unknowns A and B can be solved...