SOLUTION: Using the formula of R=log(I/Io) for Richter scale: The strongest earthquake ever to strike Japan occurred in 1933 and measure 8.4 on the Richter scale. How many times more severe

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Using the formula of R=log(I/Io) for Richter scale: The strongest earthquake ever to strike Japan occurred in 1933 and measure 8.4 on the Richter scale. How many times more severe      Log On


   

Question 1154901: Using the formula of R=log(I/Io) for Richter scale:
The strongest earthquake ever to strike Japan occurred in 1933 and measure 8.4 on the Richter scale. How many times more severe was this 1933 quake than the one in May 1983 which measured 7.1 on the Richter scale?
Answer by MathLover1(20850) About Me  (Show Source):
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R=log%28I%2FI%5Bo%5D%29 for Richter scale:
The strongest earthquake ever to strike Japan occurred in 1933 and measure R%5B1%5D=8.4 on the Richter scale.
8.4=log%28I%2FI%5Bo%5D%29
since neither+I nor I%5Bo%5D is given, let I%2FI%5Bo%5D=I%5B1%5D+
8.4=log%28I%5B1%5D%29
I%5B1%5D=10%5E8.4


1933 quake than the one in May 1983 which measured R%5B2%5D=7.1 on the Richter scale?
7.1=log%28I%2FI%5Bo%5D%29-> let I%2FI%5Bo%5D be I%5B2%5D
I%5B2%5D=10%5E7.1

How many times more severe was this 1933 quake than the one in May 1983:
I%5B1%5D%2FI%5B2%5D=10%5E8.4%2F10%5E7.1
I%5B1%5D%2FI%5B2%5D=10%5E%288.4-7.1%29
I%5B1%5D%2FI%5B2%5D=10%5E%281.3%29
I%5B1%5D%2FI%5B2%5D=19.952=>
This means that the magnitude 8.4 earthquake is 19.952 times more intense than the+7.1 magnitude earthquake.