Question 269839
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[0]}}}.



So {{{m=log((A/A[0]))}}} then becomes {{{m=log((1000000A[0]/A[0]))}}}. Cancel out the {{{A[0]}}} terms to get {{{m=log((1000000))}}}



Afterwards, rewrite {{{1000000}}} as {{{10^6}}} (since {{{10^6=1000000}}}) to get {{{m=log((10^6))}}}



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



This means that {{{m=6log((10))=6*1=6}}}



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