which of the following shows the equation $\log_4(x+6) = 2$ rewritten using logarithms?

* $4^{\log_4(x+6)} = 2^2$
* $4^{\log_4(x+6)} = 4^4$
* $\log_4(x+6) = \log_4 16$
* $\log_4(x+6) = \log_2 16$

Question

which of the following shows the equation $\log_4(x+6) = 2$ rewritten using logarithms?

* $4^{\log_4(x+6)} = 2^2$
* $4^{\log_4(x+6)} = 4^4$
* $\log_4(x+6) = \log_4 16$
* $\log_4(x+6) = \log_2 16$

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" ], "new_concepts": [ "Logarithmic Properties" ], "current_concepts": [ "Logarithmic Functions", "Logarithmic Properties" ] } ## Rewrite the constant using a logarithm of base 4 $$ 2 = \log_4(4^2) = \log_4(16) $$ ## Substitute the rewritten constant back into the equation $$ \log_4(x + 6) = \log_4(16) $$

(A) $4^{\log_4(x+6)} = 2^2$

(B) $4^{\log_4(x+6)} = 4^4$

(C) $\log_4(x+6) = \log_4 16$

(D) $\log_4(x+6) = \log_2 16$

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

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QUESTION IMAGE

Question

Explanation:

Rewrite the constant using a logarithm of base 4

Substitute the rewritten constant back into the equation

Answer: