what is the solution of $\log(t-3) = \log(17-4t)$?

$\bigcirc$ 4
$\bigcirc$ 5
$\bigcirc$ 15
$\bigcirc$ 20

Question

what is the solution of $\log(t-3) = \log(17-4t)$?

$\bigcirc$ 4
$\bigcirc$ 5
$\bigcirc$ 15
$\bigcirc$ 20

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" ] } ## Equate the logarithmic arguments Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &t - 3 = 17 - 4t \end{aligned} $$ ## Solve the linear equation for t Using the *Linear Equations* knowledge point $$ \begin{aligned} &5t = 20\ &t = 4 \end{aligned} $$ ## Verify the solution in the original domain Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &t - 3 > 0 \implies 4 - 3 = 1 > 0 \quad (\text{Valid})\ &17 - 4t > 0 \implies 17 - 16 = 1 > 0 \quad (\text{Valid}) \end{aligned} $$

(A) 4

(B) 5

(C) 15

(D) 20

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

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QUESTION IMAGE

Question

Explanation:

Equate the logarithmic arguments

Solve the linear equation for t

Verify the solution in the original domain

Answer: