The intensity of the earthquake in Oklahoma measured on the Richter scale. shows that the earthquake was 1000 times stronger the wave amplitude a of the earthquake was than.
The logarithmic function of the earthquake is given by the following formula:
R = log ( [tex]\frac{A}{Ao}[/tex] )
In this problem, the given value of R = 3, and we have to find the ratio , hence:
3 = log ( [tex]\frac{A}{Ao}[/tex] )
We can see that logarithm and power of 10 have inverse relation with each other hence, applying the power of 10 to both sides of the equality, we will get:
( [tex]\frac{A}{Ao}[/tex] ) = [tex]10^{3}[/tex] = 1000
Thus, the wave amplitude A of the earthquake was 1,000 times stronger than Ao.
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The complete question is:
An earthquake in Oklahoma measured 3.0 on the Richter scale. Use the formula R = log(4) to determine approximately how many times stronger the wave amplitude A of the earthquake was than Ao.