solve: $\log_{2}(3x + 8) = 5$
which is an equivalent equation?

$2^{5} = 3x + 8$
$5^{2} = 3x + 8$
$2^{5} = \log_{2}(3x + 8)^{2}$
$5^{2} = \log_{2}(3x + 8)^{5}$

Question

solve: $\log_{2}(3x + 8) = 5$
which is an equivalent equation?

$2^{5} = 3x + 8$
$5^{2} = 3x + 8$
$2^{5} = \log_{2}(3x + 8)^{2}$
$5^{2} = \log_{2}(3x + 8)^{5}$

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": [ "Logarithmic Functions", "Logarithmic and Exponential Inverses" ], "new_concepts": [], "current_concepts": [ "Logarithmic Functions", "Logarithmic and Exponential Inverses", "Solving Logarithmic Equations" ] } ## Identify the given logarithmic equation Using the *Logarithmic Functions* knowledge point $$ \log_{2}(3x + 8) = 5 $$ ## Apply the definition of a logarithm Using the *Logarithmic and Exponential Inverses* knowledge points $$ \log_{b}(Y) = X \iff b^X = Y $$ $$ 2^5 = 3x + 8 $$

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

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

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

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

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Logarithmic and Exponential Inverses" ] }

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Question

Explanation:

Identify the given logarithmic equation

Apply the definition of a logarithm

Answer: