A seismograph 300 km from the epicenter of an earthquake recorded a maximum amplitude of 5.7 102 µm. Find this earthquake's magnitude on the Richter scale. (Round your answer to the nearest tenth.)

To find the magnitude of an earthquake on the Richter scale, we need to use the formula:

Magnitude = log10(A/A0)

Where:
Magnitude is the Richter magnitude of the earthquake
A is the maximum amplitude (in µm) measured by the seismograph at a distance of 300 km from the epicenter
A0 is a reference amplitude of 1 µm

In this case, the maximum amplitude (A) is given as 5.7 * 10^2 µm, and A0 is 1 µm.

First, let's substitute these values into the formula:

Magnitude = log10(5.7 * 10^2 µm / 1 µm)

Next, let's simplify the expression inside the logarithm:

Magnitude = log10(5.7 * 10^2)

To evaluate this expression, we multiply 5.7 by 10 raised to the power of 2:

Magnitude = log10(570)

Using a calculator, we can find the logarithm base 10 of 570, which is approximately 2.7559. Therefore, the magnitude of the earthquake on the Richter scale is approximately 2.8 when rounded to the nearest tenth.