+157 The logarithmic function y = logx + 7.9 can be used to determine the magnitude, y, of an earthquake given an intensity comparison, x, of a previous earthquake—in this case, an earthquake with a rating of 7.9 on the Richter Scale. This function is graphed below.
What is the magnitude of an earthquake, y, that is 10 times as intense as the previous earthquake (rounded to the nearest tenth)? What intensity, x, is the aftershock with a magnitude of y = 8.7 (rounded to the nearest whole number) compared with the original 7.9 earthquake?
+129849 What is the magnitude of an earthquake, y, that is 10 times as intense as the previous earthquake (rounded to the nearest tenth)?
y = log 10 + 7.9 = 1 + 7.9 = 8.9
What intensity, x, is the aftershock with a magnitude of y = 8.7 (rounded to the nearest whole number) compared with the original 7.9 earthquake?
8.7 = log x + 7.9 subtract 7.9 from both sides
0.8 = log x
This says that x = 100.8 = about 6.3 = about 6 [rounded to the nearest whole number]
