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The general ‘rule of thumb’ used by geologists is that a thirty-fold increase in energy or intensity of an earthquake is represented by an additive increase of x on the Richter scale. A thirty-fold increase in E can be represented by E × 30n where n ∈ N. In the Richter scale formula given above, find x. One way to define the magnitude of an earthquake is to use the Richter scale formula given below: M=0.67(0.37E) + 1.46 where M is the magnitude of the earthquake on the Richter scale and E is the energy of the quake in kilowatt-hours. (1 kilowatt-hour = 3.6 × 106 Joules)
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