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
