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", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Solving Exponential Equations Algebraically" ], "new_concepts": [], "current_concepts": [ "Solving Exponential Equations Algebraically", "Logarithmic Evaluation" ] } ## Apply natural logarithm to both sides Using the *Solving Exponential Equations Algebraically* knowledge point $$ \begin{aligned} e^{3x} &= 12 \ \ln(e^{3x}) &= \ln(12) \ 3x &= \ln(12) \end{aligned} $$ ## Solve for x Using the *Solving Exponential Equations Algebraically* knowledge point $$ \begin{aligned} x &= \frac{\ln(12)}{3} \end{aligned} $$ ## Evaluate and round the decimal value Using the *Logarithmic Evaluation* knowledge point $$ \begin{aligned} \ln(12) &\approx 2.4849066 \ x &\approx \frac{2.4849066}{3} \ x &\approx 0.8283022 \ x &\approx 0.83 \end{aligned} $$

(A) $x \approx 0.83$

(B) $x \approx 1.09$

(C) $x \approx 2.48$

(D) $x \approx 7.44$

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

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QUESTION IMAGE

Question

Explanation:

Apply natural logarithm to both sides

Solve for x

Evaluate and round the decimal value

Answer: