To determine the magnitude, [tex]\( M \)[/tex], of an earthquake that is 35 times more intense than a standard earthquake, we use the provided formula:
[tex]\[ M = \log \frac{I}{S} \][/tex]
Here:
- [tex]\( I \)[/tex] is the intensity of the earthquake, which is 35 times that of the standard earthquake.
- [tex]\( S \)[/tex] is the intensity of a "standard" earthquake.
Substituting the given values into the formula, we have:
[tex]\[ M = \log \frac{35}{1} \][/tex]
[tex]\[ M = \log 35 \][/tex]
Using a calculator to find the logarithm base 10 of 35:
[tex]\[ \log 35 \approx 1.544068 \][/tex]
Rounding 1.544068 to the nearest tenth, we get:
[tex]\[ M \approx 1.5 \][/tex]
Therefore, the magnitude of the earthquake is:
[tex]\[ M \approx 1.5 \][/tex]
So, the correct answer is:
[tex]\[ 1.5 \][/tex]
