which of the following is the inverse of (y = 12^x)?

(y = log_{\frac{1}{12}} x)

(y = log_{12} \frac{1}{x})

(y = log_x 12)

(y = log_{12} x)

Question

which of the following is the inverse of (y = 12^x)?

(y = log_{\frac{1}{12}} x)

(y = log_{12} \frac{1}{x})

(y = log_x 12)

(y = log_{12} x)

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Inverse Functions", "Exponential Inverse" ], "new_concepts": [], "current_concepts": [ "Inverse Functions", "Exponential Inverse", "Logarithmic Functions" ] } ## Swap variables to find the inverse $$ x = 12^y $$ ## Solve for y using logarithms $$ y = \log_{12} x $$

(A) $y = \log_{\frac{1}{12}} x$

(B) $y = \log_{12} \frac{1}{x}$

(C) $y = \log_x 12$

(D) $y = \log_{12} x$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Exponential Inverse" ] }

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QUESTION IMAGE

Question

Explanation:

Swap variables to find the inverse

Solve for y using logarithms

Answer: