what is the solution to the equation below?

\3\log_{4} x = \log_{4} 32 + \log_{4} 2\

$x = -8$
$x = -4$
$x = 4$
$x = 8$

Question

what is the solution to the equation below?

\3\log_{4} x = \log_{4} 32 + \log_{4} 2\

$x = -8$
$x = -4$
$x = 4$
$x = 8$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Logarithmic Properties", "Logarithmic Equations" ], "new_concepts": [], "current_concepts": [ "Logarithmic Properties", "Logarithmic Equations" ] } ## Apply logarithmic properties to simplify both sides $$ \begin{aligned} \log_4(x^3) &= \log_4(32 \cdot 2) \ \log_4(x^3) &= \log_4(64) \end{aligned} $$ ## Solve for x $$ \begin{aligned} x^3 &= 64 \ x &= \sqrt[3]{64} \ x &= 4 \end{aligned} $$ ## Verify the solution $$ \begin{aligned} x = 4 &> 0 \quad \text{(valid domain)} \end{aligned} $$

$x = -8$

$x = -4$

$x = 4$

$x = 8$

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

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Question

Explanation:

Apply logarithmic properties to simplify both sides

Solve for x

Verify the solution

Answer: