which logarithmic equation has the same solution as $x-4 = 2^3$?

* $\log 3^2 = (x-4)$
* $\log 2^3 = (x-4)$
* $\log_2(x-4) = 3$
* $\log_3(x-4) = 2$

Question

which logarithmic equation has the same solution as $x-4 = 2^3$?

* $\log 3^2 = (x-4)$
* $\log 2^3 = (x-4)$
* $\log_2(x-4) = 3$
* $\log_3(x-4) = 2$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Logarithmic Functions", "Exponential Inverse" ], "new_concepts": [], "current_concepts": [ "Logarithmic Functions", "Exponential Inverse" ] } ## Convert exponential equation to logarithmic form $$ \begin{aligned} &y = b^x \iff \log_b(y) = x \ &x - 4 = 2^3 \iff \log_2(x - 4) = 3 \end{aligned} $$ ## Verify the solution of both equations $$ \begin{aligned} &x - 4 = 8 \implies x = 12 \ &\log_2(12 - 4) = \log_2(8) = 3 \end{aligned} $$

(A) $\log 3^2 = (x-4)$

(B) $\log 2^3 = (x-4)$

(C) $\log_2(x-4) = 3$

(D) $\log_3(x-4) = 2$

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

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Question

Explanation:

Convert exponential equation to logarithmic form

Verify the solution of both equations

Answer: