Problem
The Richter scale measures the intensity, or magnitude, of an earthquake. The formula for the magnitude $R$ of an earthquake is $R=\log \left(\frac{a}{T}\right)+B$, where a is the amplitude in micrometers of the vertical motion of the ground at the recording station, $T$ is the number of seconds between successive seismic waves, and $B$ is an adjustment factor that takes into account the weakening of the seismic wave as the distance increases from the epicenter of the earthquake. Use the Richter scale formula to find the magnitude R of the earthquake given that the amplitude is 270 micrometers, the time between waves is 1.5 seconds, and $B$ is 2.1 . $R=\square$ (Round to the nearest tenth as needed.)
Solution
Step 1 ：We are given the values of $a$, $T$, and $B$ and we are asked to find the value of $R$. We can substitute these values into the formula $R=\log \left(\frac{a}{T}\right)+B$ and calculate the result.
Step 2 ：Substitute $a = 270$, $T = 1.5$, and $B = 2.1$ into the formula.
Step 3 ：Calculate $R = \log \left(\frac{270}{1.5}\right)+2.1$.
Step 4 ：Calculate $R = 4.355272505103306$.
Step 5 ：Round $R$ to the nearest tenth to get the final answer.
Step 6 ：Final Answer: \(\boxed{4.4}\)
