what is the solution of $\log(2t+4) = \log(14-3t)$?

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Question

what is the solution of $\log(2t+4) = \log(14-3t)$?

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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", "Linear Equations" ], "new_concepts": [], "current_concepts": [ "Solving Logarithmic Equations", "Linear Equations" ] } ## Equate the arguments Using the *Solving Logarithmic Equations* knowledge point $$ 2t + 4 = 14 - 3t $$ ## Solve the linear equation Using the *Linear Equations* knowledge point $$ \begin{aligned} 5t + 4 &= 14 \ 5t &= 10 \ t &= 2 \end{aligned} $$ ## Verify the solution Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} 2(2) + 4 &= 8 > 0 \ 14 - 3(2) &= 8 > 0 \end{aligned} $$

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

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QUESTION IMAGE

Question

Explanation:

Equate the arguments

Solve the linear equation

Verify the solution

Answer: