an earthquake with a rating of 7.9 is known t...
an earthquake with a rating of 7.9 is known to be a great earthquake that can cause damage that extends several hundred kilometers. r = log x r = rating of the earthquakes size on the richter scale x = ratio of earthquake intensity to a minimum level of intensity what is the value of x when the richter scale rating is 7.9? round your answer to the nearest hundredth. enter the correct answer. 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.
Answer
# Explanation:
## Step1: Substitute R value
Given $R = \log x$ and $R = 7.9$, we substitute to get $7.9=\log x$. Since the base of the common - log is 10, we can write it as $7.9=\log_{10}x$.
## Step2: Convert from log to exponential form
By the definition of logarithms, if $y = \log_{a}x$, then $x=a^{y}$. Here, $a = 10$, $y = 7.9$, so $x = 10^{7.9}$.
## Step3: Calculate the value of x
Using a calculator, $10^{7.9}\approx7943282.35$.
# Answer:
$7943282.35$