Question

The Richter scale magnitude reading m is given by m=log10x , where x represents the amplitude of the seismic wave causing ground motion. Determine the reading of an earthquake that is 10 times less intense than an earthquake that measures 4.5 on the Richter scale.

Answer 1

The Richter scale magnitude reading m is given by the equation m = log10(x), where x represents the amplitude of the seismic wave causing ground motion. To determine the reading of an earthquake that is 10 times less intense than an earthquake measuring 4.5 on the Richter scale, we can use the fact that the Richter scale is logarithmic.

Step-by-step explanation:

The Richter scale magnitude reading m is given by the equation m = log10(x), where x represents the amplitude of the seismic wave causing ground motion. To determine the reading of an earthquake that is 10 times less intense than an earthquake measuring 4.5 on the Richter scale, we can use the fact that the Richter scale is logarithmic.

If an earthquake measures 4.5 on the Richter scale, the intensity can be represented as x = 10^(4.5). To find the reading for an earthquake that is 10 times less intense, we need to find the value of m when x is 1/10th of the original value.

Let's substitute x with 10^(4.5) into the equation and simplify:

m = log10(10^(4.5)/10)

m = log10(10^(4.5 - 1))

m = log10(10^(3.5))

m = 3.5

Therefore, an earthquake that is 10 times less intense than an earthquake measuring 4.5 on the Richter scale would have a reading of 3.5.

Answer 2

Answer: The reading would be 5.5 on the Richter scale.

Step-by-step explanation:

The intensity of an earthquake that measures 4.5 on the Ritcher scale can be found by solving:

4.5 = log₁₀(x)

for x.

remember that:

logₐ(x) = ln(x)/ln(a)

Then we can rewrite our equation as:

4.5 = ln(x)/ln(10)

4.5*ln(10) = ln(x)

we also know that:

ln(exp(x)) = exp(ln(x)) = x

Then we can apply the exponential equation to both sides to get:

exp( 4.5*ln(10)) = exp( ln(x) ) = x

exp( 4.5*ln(10)) = x

x = 31,622.8

Now, if we have an intensity 10 times larger than this, we will have:

x = 10*31,622.8 = 316,228

The reading on the Richter scale will be:

m = Log₁₀(316,228) = 5.5