Question

PRACTICE ANOTHER This exercise uses elementary properties of the Richter Scale. One earthquake has a Richter scale reading of 6.5. A second is 10000 times as strong. What is its Richter scale reading?

Answer 1

The Richter scale is used to measure the energy produced by an earthquake. Each increase of one unit on the scale represents a tenfold increase in energy released. To find the Richter scale reading of a second earthquake that is 10000 times stronger, we solve the exponential equation 10^x = 10000.

Step-by-step explanation:

The Richter scale is used to measure the energy produced by an earthquake. It is a logarithmic scale, meaning that each increase of one unit on the scale represents a tenfold increase in energy released. In this question, the first earthquake has a Richter scale reading of 6.5, and the second earthquake is 10000 times stronger. To find its Richter scale reading, we need to determine how many times 10 is raised to achieve a factor of 10000. We can write this as an exponential equation: 10x = 10000.

By taking the logarithm base 10 of both sides of the equation, we can solve for x:

x = log10(10000) = 4.

Therefore, the second earthquake has a Richter scale reading of 6.5 + 4 = 10.5.

Answer 2

In this case, the Richter scale reading of the second earthquake can be calculated using logarithms which is 9.5.

Step-by-step explanation:

The Richter scale is a logarithmic scale used to quantify the energy produced by an earthquake. The numbers on the Richter scale represent the amplitude of seismic waves, which is directly related to the energy released by the earthquake.

In this question, we are given that one earthquake has a Richter scale reading of 6.5. The second earthquake is stated to be 10000 times as strong as the first one.

Since the Richter scale is logarithmic, we can use logarithms to calculate the Richter scale reading of the second earthquake.

Let's denote the Richter scale reading of the second earthquake as x. We know that the second earthquake is 10000 times as strong as the first one, so we can set up the equation 10^(x-6.5) = 10000.

Solving this equation, we find x = 9.5. Therefore, the Richter scale reading of the second earthquake is 9.5.