Question 1112055
the formula for richter scale is R = (I/S)


let the intensity of the alaska earthquake be represented by A.


let the intensity of the california earthquake be represented by C.


the formula for alaska becomes 9.5 = log(A/S).


the formula for california becomes 6.4 = log(C/S).


the definition of logs states that y = logb(x) if and only if b^y = x.


remember that log, by itself, means log10, which means log to the base of 10.


therefore y = log(x) is the same asy = log10(x) and the logarithm definition states that:


y = log10(x) if and only if 10^y = x.


using this definition for alaska gets us:


9.5 = log(A/S) if and only if 10^9.5 = A/S.


solve for A to get A = S * 10^9.


using this definition for california gets us:


6.4 = log(C/S) if and only if 10^6.4 = C/S.


solve for C to get C = S * 10^6.4


how many times the intensity of the alaska earthquake is compared to the intensity of the california earthqube becomes A/C.


A/C becomes (10^9.5 * S) / (10^6.4 * S)


the S in the numerator and the denominator cancel out and you are left with:


A/C = 10^9.5 / 10^6.4.


since b^x / b^y = b^(x-y), then you get:


10^9.5 / 10^6.4 = 10^(9.5-6.4) which results in A/C = 10^3.1.


solve for A/C to get A/C = 1258.925412.


knowing how the formulas work, you could have simply subtracted 6.4 from 9.5 and gotten 3.1 and then taken 10^3.1 directly to get the same answer.


remember, each increase of 1 on the richter scale is 10 times more powerful.


going from 6.4 to 7.4 gets you 7.4 is 10^1 times as powerful as 6.4.


going from 7.4 to 8.4 get you 8.4 is 10^1 times as powerful as 7.4 which is 10^1 times as powerful as 6.4.


going from 8.4 to 9.4 gets you 9.4 is 10^1 times as powerful as 8.4 which is 10^1 times as powerful as 7.4 which is 10^1 times as powerful as 6.4.


going from 9.4 to 9.5 gets you 9.5 is 10^.1 times as powerful as 9.4 which is 10^1 times as powerful as 8.4 which is 10^1 times as powerful as 7.4 which is 10^1 times as powerful as 6.4


what this says is that 9.5 is 10^.1 * 10^1 * 10^1 * 10^1 as powerful as 6.4.


if you remember your exponent arithmetic formulas, you know that b^x * b^y = b^(x+y), therefore 10^.1 * 10^1 * 10^1 * 10^1 is equal to 10^(.1 + 1 + 1 = 1) which is equal to 10^3.1 which is equal to 1258.925412.


the intensity of the alaska earthquake was 1258.925412 times the intensity of the california earthquake.