solve: \ln 2x + \ln 2 = 0

x =

Question

solve: \ln 2x + \ln 2 = 0

x =

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Logarithmic Product Rule", "Solving Logarithmic Equations" ], "new_concepts": [], "current_concepts": [ "Logarithmic Product Rule", "Solving Logarithmic Equations" ] } ## Apply the logarithmic product rule Using the *Logarithmic Product Rule* knowledge point $$ \begin{aligned} &\ln(2x) + \ln(2) = 0 \ &\ln(2x \cdot 2) = 0 \ &\ln(4x) = 0 \end{aligned} $$ ## Convert to exponential form Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &4x = e^0 \ &4x = 1 \end{aligned} $$ ## Solve for x Using the *Linear Equations* knowledge point $$ \begin{aligned} &x = \frac{1}{4} \end{aligned} $$ Solve: $\ln 2x + \ln 2 = 0$ $x =$ $\frac{1}{4}$ { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Algebra", "Solving Logarithmic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Apply the logarithmic product rule

Convert to exponential form

Solve for x

Answer: