the magnitude, $m$, of an earthquake is defined to be $m = \log \frac{i}{s}$, where $i$ is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and $s$ is the intensity of a \standard\ earthquake, which is barely detectable. what is the magnitude of an earthquake that is 35 times more intense than a standard earthquake? use a calculator. round your answer to the nearest tenth.

$\bigcirc$ -1.5
$\bigcirc$ -0.5
$\bigcirc$ 1.5
$\bigcirc$ 3.6

Question

the magnitude, $m$, of an earthquake is defined to be $m = \log \frac{i}{s}$, where $i$ is the intensity of the earthquake (measured by the amplitude of the seismograph wave) and $s$ is the intensity of a \standard\ earthquake, which is barely detectable. what is the magnitude of an earthquake that is 35 times more intense than a standard earthquake? use a calculator. round your answer to the nearest tenth.

$\bigcirc$ -1.5
$\bigcirc$ -0.5
$\bigcirc$ 1.5
$\bigcirc$ 3.6

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Logarithmic Evaluation" ], "new_concepts": [], "current_concepts": [ "Logarithmic Evaluation", "Logarithmic Functions" ] } ## Identify the given values and formula Using the *Logarithmic Evaluation* knowledge point $$ \begin{aligned} &M = \log \frac{I}{S}\ &I = 35S \implies \frac{I}{S} = 35 \end{aligned} $$ ## Calculate the magnitude Using the *Logarithmic Evaluation* knowledge point $$ \begin{aligned} &M = \log(35)\ &M \approx 1.544\ &M \approx 1.5 \quad (\text{rounded to the nearest tenth}) \end{aligned} $$

(A) $-1.5$

(B) $-0.5$

(C) $1.5$

(D) $3.6$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Logarithmic Evaluation" ] }

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Question

Explanation:

Identify the given values and formula

Calculate the magnitude

Answer: