which equation(s) have $x = 2$ as the solution?

$\log_{2}(5x + 6) = 4$
$\log_{x}16 = 4$
$\log_{3}(6x + 4) = 3$
$\log_{x}36 = 6$

Question

which equation(s) have $x = 2$ as the solution?

$\log_{2}(5x + 6) = 4$
  $\log_{x}16 = 4$
  $\log_{3}(6x + 4) = 3$
  $\log_{x}36 = 6$

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" ] } ## Evaluate the first equation Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &\text{Substitute } x = 2 \text{ into } \log_2(5x + 6) = 4:\ &\log_2(5(2) + 6) = \log_2(10 + 6) = \log_2(16)\ &\log_2(16) = 4 \quad (4 = 4) \end{aligned} $$ ## Evaluate the second equation Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &\text{Substitute } x = 2 \text{ into } \log_x 16 = 4:\ &\log_2 16 = 4 \quad (4 = 4) \end{aligned} $$ ## Evaluate the third equation Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &\text{Substitute } x = 2 \text{ into } \log_3(6x + 4) = 3:\ &\log_3(6(2) + 4) = \log_3(12 + 4) = \log_3(16)\ &\log_3(16) e 3 \quad (\text{since } 3^3 = 27) \end{aligned} $$ ## Evaluate the fourth equation Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &\text{Substitute } x = 2 \text{ into } \log_x 36 = 6:\ &\log_2 36 e 6 \quad (\text{since } 2^6 = 64) \end{aligned} $$

(A) $\log_2(5x + 6) = 4$

(B) $\log_x 16 = 4$

(C) $\log_3(6x + 4) = 3$

(D) $\log_x 36 = 6$

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

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QUESTION IMAGE

Question

Explanation:

Evaluate the first equation

Evaluate the second equation

Evaluate the third equation

Evaluate the fourth equation

Answer: