SOLUTION: The intensity levels I of two earthquakes measured on a seismograph can be compared by the formula log I1 I2 = M1 − M2 where M is the magnitude given by the Richter s

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Question 1153141: The intensity levels I of two earthquakes measured on a seismograph can be compared by the formula
log
I1
I2
= M1 − M2
where M is the magnitude given by the Richter scale. An earthquake of magnitude 6.4 hit a city. Two years later, that same region experienced yet another, more devastating earthquake, this time with a magnitude of 8.0. How many times greater was the intensity of the second earthquake? Round to the nearest whole number.
times greater

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
log%28I%5B1%5D%2FI%5B2%5D%29=+M%5B1%5D+%E2%88%92+M%5B2%5D
given: M%5B1%5D=8.0 and M%5B2%5D=6.4
log%28I%5B1%5D%2FI%5B2%5D%29=+8.0+-6.4
log%28I%5B1%5D%2FI%5B2%5D%29=+1.6
I%5B1%5D%2FI%5B2%5D=antilog%281.6%29
I%5B1%5D%2FI%5B2%5D=39.8107240

or this way:
log%28I%5B1%5D%29=8.0
I%5B1%5D=antilog%288.0%29
I%5B1%5D=100000000
log%28I%5B2%5D%29=6.4
I%5B2%5D=antilog%286.4%29
I%5B2%5D=2511886.4

I%5B1%5D%2FI%5B2%5D=100000000%2F2511886.4=39.8107240