Logrithmetic Problem question
Last week there was an earthquake that measured as a magnitude of 3.2 on the Richter scale. Today you hear on the radio that there was a second earthquake that was 27 times more intense than the first. What was the magnitude of the second earthquake on the Richter scale?
To find the magnitude of the second earthquake on the Richter scale, we can use the formula:
M2 = M1 + log10(A2 / A1)
Where:
M2 = magnitude of the second earthquake
M1 = magnitude of the first earthquake
A2 = intensity of the second earthquake
A1 = intensity of the first earthquake
We know that the first earthquake has a magnitude (M1) of 3.2 on the Richter scale. Since the second earthquake is 27 times more intense than the first, we can say that A2 = 27 * A1.
Therefore, the equation becomes:
M2 = 3.2 + log10(27 * A1 / A1)
Simplifying:
M2 = 3.2 + log10(27)
Using a calculator or log tables, we find that log10(27) is approximately 1.431.
Therefore:
M2 = 3.2 + 1.431
M2 ≈ 4.631
So, the magnitude of the second earthquake on the Richter scale is approximately 4.631.
To find the magnitude of the second earthquake on the Richter scale, we can use the formula:
Magnitude2 = Magnitude1 + log(base 10)(Intensity2 / Intensity1),
where Magnitude1 is the magnitude of the first earthquake, Intensity2 is the intensity of the second earthquake, and Intensity1 is the intensity of the first earthquake.
In this case, the problem states that the second earthquake was 27 times more intense than the first. So, we can represent this as:
Intensity2 = 27 * Intensity1.
Since we are given the magnitude of the first earthquake (Magnitude1 = 3.2), we need to convert it to intensity using the formula:
Intensity1 = 10^(1.5 * Magnitude1).
Now we can substitute the values into the formula to calculate the magnitude of the second earthquake:
Magnitude2 = 3.2 + log(base 10)(27 * Intensity1 / Intensity1).
Simplifying the equation:
Magnitude2 = 3.2 + log(base 10)(27).
Using logarithmic properties:
Magnitude2 = 3.2 + log(base 10)(3^3).
Again using logarithmic properties, we know that log(base 10)(10^n) = n, so:
Magnitude2 = 3.2 + 3.
Therefore, the magnitude of the second earthquake on the Richter scale is:
Magnitude2 = 6.2.
depends what you mean by intense.
If amplitude is 27 times
log A = 3.2
so A =1584
B = 1584 * 27 = 42792
log B = 4.63