solve: $\log_2(3x + 8) = 5$
which is an equivalent equation?
$2^5 = 3x + 8$
$5^2 = 3x + 8$
$2^5 = \log_2(3x + 8)^2$
$5^2 = \log_2(3x + 8)^5$
$x = $

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Accepted Answer

{ "quality": "clear", "question_count": 2, "skills_matched": [ "step_cot", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Logarithmic Functions", "Logarithmic and Exponential Inverses", "Linear Equations" ], "new_concepts": [ "Solving Logarithmic Equations" ], "current_concepts": [ "Logarithmic Functions", "Logarithmic and Exponential Inverses", "Solving Logarithmic Equations", "Linear Equations" ] } ## Convert to exponential form Using the *Logarithmic and Exponential Inverses* knowledge point $$ \log_{b}(y) = x \iff b^x = y $$ $$ 2^5 = 3x + 8 $$ ## Solve the linear equation Using the *Linear Equations* knowledge point $$ \begin{aligned} 32 &= 3x + 8 \ 24 &= 3x \ x &= 8 \end{aligned} $$ ## Question 1 (A) $2^5 = 3x + 8$

(B) $5^2 = 3x + 8$

(C) $2^5 = [\log_2(3x + 8)]^2$

(D) $5^2 = [\log_2(3x + 8)]^5$ ## Question 2 $x =$ 8 { "subject": "Mathematics", "question_type": "Multi-part", "knowledge_point": [ "Mathematics", "Algebra", "Solving Logarithmic Equations" ] }

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Explanation:

Convert to exponential form

Solve the linear equation

Answer:

Question 1

Question 2