An earthquake in Oklahoma measured 3.0 on the Richter scale Use the formula R=log((A)/(A_(0))) to determine approximately how many times stronger the wave amplitude A of the earthquake was than A_(0) Aapprox 0.48A_(0) A=1,000A_(0) Aapprox 20.1A_(0) A=3,000A_(0)

## Step 1<br />The Richter scale is a logarithmic scale used to measure the intensity of earthquakes. The formula given, \(R = \log(\frac{A}{A_{0}})\), is used to calculate the amplitude of the seismic waves (A) relative to a reference amplitude (A0). The logarithmic nature of the formula means that each whole number increase on the Richter scale corresponds to a tenfold increase in the amplitude of the seismic waves.<br /><br />## Step 2<br />Given that the earthquake in Oklahoma measured 3.0 on the Richter scale, we can substitute this value into the formula to find the relative amplitude of the seismic waves.<br /><br />### \(3 = \log(\frac{A}{A_{0}})\)<br /><br />## Step 3<br />To solve for A, we need to convert the logarithmic equation to an exponential equation. This is done by using the property of logarithms that states \(\log_{b}x = y\) is equivalent to \(b^{y} = x\).<br /><br />### \(10^{3} = \frac{A}{A_{0}}\)<br /><br />## Step 4<br />Finally, we solve for A by multiplying both sides of the equation by \(A_{0}\).<br /><br />### \(A = 10^{3}A_{0}\)