an earthquake with a rating of 3.8 can cause ...
an earthquake with a rating of 3.8 can cause destruction in areas of up to 100 kilometers that are populated. r = log x r = rating of the earthquakes size on the richter scale x = ratio of earthquake intensity to a minimum level of intensity 1) substitute known values into the equation. 2) raise each side of the equation as the power of the base of the log. 3) simplify using the property. what is the value of x when the richter scale rating is 3.8? round your answer to the nearest hundredth. enter the correct answer.
Answer
# Explanation:
## Step1: Substitute R value
Given $R = \log x$ and $R = 3.8$, we substitute $R$ to get $3.8=\log x$. Since the base of the common - log is 10, we can write it as $3.8=\log_{10}x$.
## Step2: Convert from log form to exponential form
By the definition of logarithms, if $y = \log_{a}x$, then $x=a^{y}$. Here $a = 10$, $y = 3.8$, so $x = 10^{3.8}$.
## Step3: Calculate the value of x
Using a calculator, $10^{3.8}\approx6309.57$.
# Answer:
$6309.57$