which equation(s) have $x = 2$ as the solution?
$\log_{2}(5x + 6) = 4$
$\log_{x}16 = 4$
$\log_{3}(6x + 4) = 3$
$\log_{x}36 = 6$

which equation(s) have $x = -3$ as the solution?
$\log_{3}(2x + 15) = 2$
$\log_{5}(8x + 9) = 2$
$\log_{4}(-20x + 4) = 3$
$\log_{x}81 = 4$

Question

which equation(s) have $x = 2$ as the solution?
$\log_{2}(5x + 6) = 4$
$\log_{x}16 = 4$
$\log_{3}(6x + 4) = 3$
$\log_{x}36 = 6$

which equation(s) have $x = -3$ as the solution?
$\log_{3}(2x + 15) = 2$
$\log_{5}(8x + 9) = 2$
$\log_{4}(-20x + 4) = 3$
$\log_{x}81 = 4$

Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "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 question for $x = 2$ Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &\text{For }\log_2(5x + 6) = 4:\ &\log_2(5(2) + 6) = \log_2(16) = 4 \quad (\text{True})\ &\text{For }\log_x 16 = 4:\ &\log_2 16 = 4 \quad (\text{True})\ &\text{For }\log_3(6x + 4) = 3:\ &\log_3(6(2) + 4) = \log_3(16) e 3 \quad (\text{False})\ &\text{For }\log_x 36 = 6:\ &\log_2 36 e 6 \quad (\text{False}) \end{aligned} $$ ## Evaluate the second question for $x = -3$ Using the *Solving Logarithmic Equations* knowledge point $$ \begin{aligned} &\text{For }\log_3(2x + 15) = 2:\ &\log_3(2(-3) + 15) = \log_3(9) = 2 \quad (\text{True})\ &\text{For }\log_5(8x + 9) = 2:\ &\log_5(8(-3) + 9) = \log_5(-15) \quad (\text{Undefined, False})\ &\text{For }\log_4(-20x + 4) = 3:\ &\log_4(-20(-3) + 4) = \log_4(64) = 3 \quad (\text{True})\ &\text{For }\log_x 81 = 4:\ &\log_{-3} 81 \quad (\text{Base must be positive, False}) \end{aligned} $$ ## Question 1 The equations that have $x = 2$ as a solution are: * $\log_2(5x + 6) = 4$ * $\log_x 16 = 4$ ## Question 2 The equations that have $x = -3$ as a solution are: * $\log_3(2x + 15) = 2$ * $\log_4(-20x + 4) = 3$ { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Solving Logarithmic Equations" ] }

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QUESTION IMAGE

Question

Explanation:

Evaluate the first question for \(x = 2\)

Evaluate the second question for \(x = -3\)

Answer:

Question 1

Question 2