SOLUTION: The Richter magnitude (m) of an earthquake is given by the formula: m = log A/Ao (o is subscript for 0) where A is the maximum amplitude of the earthquake and Ao is the co

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: The Richter magnitude (m) of an earthquake is given by the formula: m = log A/Ao (o is subscript for 0) where A is the maximum amplitude of the earthquake and Ao is the co      Log On


   

Question 269839: The Richter magnitude (m) of an earthquake is given by the formula:
m = log A/Ao
(o is subscript for 0)
where A is the maximum amplitude of the earthquake and Ao is the constant. What is the magnitude on the Richter scale of an earthquake with an amplitude that is a million times Ao?
I know that A=1000000, but am unsure as to what to do with Ao. There isn't anything about it in my book, so I am unsure as to what to do with this particular logarithmic equation. Help explaining this would be extremely appreciated!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If "A is the maximum amplitude of the earthquake and Ao is the constant." and "the magnitude on the Richter scale of an earthquake with an amplitude that is a million times Ao", this means that A=1000000A%5B0%5D.


So m=log%28%28A%2FA%5B0%5D%29%29 then becomes m=log%28%281000000A%5B0%5D%2FA%5B0%5D%29%29. Cancel out the A%5B0%5D terms to get m=log%28%281000000%29%29


Afterwards, rewrite 1000000 as 10%5E6 (since 10%5E6=1000000) to get m=log%28%2810%5E6%29%29


Next, pull down the exponent to get m=6log%28%2810%29%29. Finally, evaluate the log of 10 (we're in base 10) to get 1. Ie log%28%2810%29%29=1 where the base is 10.


This means that m=6log%28%2810%29%29=6%2A1=6


In the end, this means that m=6. So the magnitude is 6.0 on the Richter scale.