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.

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

5

step-by-step explanation: