omar wants to use a graph to solve the equation below.

$\log_{6} x = \log_{2}(x+4)$

which system of equations should omar use?

$y_1 = \frac{\log 6}{x}, y_2 = \frac{\log 2}{x+4}$

$y_1 = \frac{\log x}{\log 6}, y_2 = \frac{\log x + 4}{\log 2}$

$y_1 = \frac{\log 6}{\log 2}, y_2 = \frac{\log x}{\log(x+4)}$

$y_1 = \frac{\log x}{\log 6}, y_2 = \frac{\log(x+4)}{\log 2}$

Question

omar wants to use a graph to solve the equation below.

$\log_{6} x = \log_{2}(x+4)$

which system of equations should omar use?

$y_1 = \frac{\log 6}{x}, y_2 = \frac{\log 2}{x+4}$

$y_1 = \frac{\log x}{\log 6}, y_2 = \frac{\log x + 4}{\log 2}$

$y_1 = \frac{\log 6}{\log 2}, y_2 = \frac{\log x}{\log(x+4)}$

$y_1 = \frac{\log x}{\log 6}, y_2 = \frac{\log(x+4)}{\log 2}$

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Change of Base Formula", "Graphical Solutions of Equations" ], "new_concepts": [], "current_concepts": [ "Change of Base Formula", "Graphical Solutions of Equations", "Logarithmic Functions" ] } ## Define the system of equations $$ \begin{aligned} &y_1 = \log_{6} x \ &y_2 = \log_{2} (x + 4) \end{aligned} $$ ## Apply the change of base formula $$ \begin{aligned} &y_1 = \frac{\log x}{\log 6} \ &y_2 = \frac{\log(x + 4)}{\log 2} \end{aligned} $$

(A) $y_1 = \frac{\log 6}{x}, y_2 = \frac{\log 2}{x+4}$

(B) $y_1 = \frac{\log x}{\log 6}, y_2 = \frac{\log x + 4}{\log 2}$

(C) $y_1 = \frac{\log 6}{\log 2}, y_2 = \frac{\log x}{\log(x+4)}$

(D) $y_1 = \frac{\log x}{\log 6}, y_2 = \frac{\log(x+4)}{\log 2}$

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Change of Base Formula" ] }

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QUESTION IMAGE

Question

Explanation:

Define the system of equations

Apply the change of base formula

Answer: