what is the true solution to $2 \ln 4x = 2 \ln 8$?

$x = -4$
$x = -2$
$x = 2$
$x = 4$

Question

what is the true solution to $2 \ln 4x = 2 \ln 8$?

$x = -4$
$x = -2$
$x = 2$
$x = 4$

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 Logarithmic Equations" ], "new_concepts": [], "current_concepts": [ "Solving Logarithmic Equations", "Logarithmic Functions" ] } ## Simplify the equation Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} 2 \ln(4x) &= 2 \ln(8) \ \ln(4x) &= \ln(8) \end{aligned} $$ ## Solve for x Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} 4x &= 8 \ x &= 2 \end{aligned} $$ ## Verify the solution Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} \text{For } x = 2, \quad 4x = 8 > 0 \end{aligned} $$

$x = -4$

$x = -2$

$x = 2$

$x = 4$

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

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Simplify the equation

Solve for x

Verify the solution

Answer: