which of the following is the inverse of $y = 6^x$?

* $y = \log_6 x$
* $y = \log_x 6$
* $y = \log_{\frac{1}{6}} x$
* $y = \log_6 6x$

Question

which of the following is the inverse of $y = 6^x$?

* $y = \log_6 x$
* $y = \log_x 6$
* $y = \log_{\frac{1}{6}} x$
* $y = \log_6 6x$

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 and Exponential Inverses" ], "new_concepts": [], "current_concepts": [ "Logarithmic and Exponential Inverses", "Inverse Functions" ] } ## Swap variables to find the inverse Using the *Logarithmic and Exponential Inverses* knowledge point $$ x = 6^y $$ ## Solve for y using logarithms Using the *Logarithmic and Exponential Inverses* knowledge point $$ y = \log_{6}x $$

(A) $y = \log_{6}x$

(B) $y = \log_{x}6$

(C) $y = \log_{\frac{1}{6}}x$

(D) $y = \log_{6}6x$

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

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QUESTION IMAGE

Question

Explanation:

Swap variables to find the inverse

Solve for y using logarithms

Answer: