The magnitude of an earthquake is defined as M=log(A / A_{0}), where A is the amplitude of the ground motion and A_{0} is the amplitude corrected for the distance from the actual earthquake that would be expected for a 'standard earthquake'. On March 2, 2012, an earthquake with an amplitude 10^{5.1} times A_{0 }was recorded in Norman Wells, North West Territories. Meanwhile, on October 12, 2012, off the shore of Haida Gwaii, British Columbia, there was another earthquake with an amplitude 10^{7.7} times A_{0}.

Algebraically determine, based on their Richter scale magnitudes, how much stronger the Haida gwaii earthquake was (to the nearest whole number).

Thank you.

Guest Jun 8, 2022