what is the solution of $\log_{2}(3x - 7) = 3$?

* $\frac{1}{3}$
* $4$
* $5$
* $\frac{16}{3}$

Question

what is the solution of $\log_{2}(3x - 7) = 3$?

* $\frac{1}{3}$
* $4$
* $5$
* $\frac{16}{3}$

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" ] } ## Convert to exponential form Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &\log_{2}(3x - 7) = 3 \ &3x - 7 = 2^3 \ &3x - 7 = 8 \end{aligned} $$ ## Solve for x Using the *Linear Equations* knowledge point $$ \begin{aligned} &3x = 8 + 7 \ &3x = 15 \ &x = 5 \end{aligned} $$ ## Verify the solution Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &3(5) - 7 = 15 - 7 = 8 > 0 \ &\log_{2}(8) = 3 \end{aligned} $$

(A) $\frac{1}{3}$

(B) 4

(C) 5

(D) $\frac{16}{3}$

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

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