what is the solution to the equation $e^{3x} = 12$? round your answer to the nearest hundredth.

$x = 0.83$
$x = 1.09$
$x = 2.48$
$x = 7.44$

Question

what is the solution to the equation $e^{3x} = 12$? round your answer to the nearest hundredth.

$x = 0.83$
$x = 1.09$
$x = 2.48$
$x = 7.44$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Exponential Equations", "Logarithmic Properties" ], "new_concepts": [], "current_concepts": [ "Exponential Equations", "Logarithmic Properties" ] } ## Take the natural logarithm of both sides $$ \ln(e^{3x}) = \ln(12) $$ ## Simplify using logarithm properties $$ 3x = \ln(12) $$ ## Solve for x and round to the nearest hundredth $$ \begin{aligned} x &= \frac{\ln(12)}{3} \ x &\approx \frac{2.4849}{3} \ x &\approx 0.8283 \approx 0.83 \end{aligned} $$

(A) $x = 0.83$

(B) $x = 1.09$

(C) $x = 2.48$

(D) $x = 7.44$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Take the natural logarithm of both sides

Simplify using logarithm properties

Solve for x and round to the nearest hundredth

Answer: