which system of equations could be graphed to solve the equation below?

$\log_{0.5} x = \log_{3} 2 + x$

$y_1 = \frac{\log 0.5}{x}, y_2 = \frac{\log 3}{2+x}$

$y_1 = \frac{\log x}{\log 0.5}, y_2 = \frac{\log 2+x}{\log 3}$

$y_1 = \frac{\log 0.5}{\log 3}, y_2 = \frac{\log x}{\log 2+x}$

$y_1 = \frac{\log x}{\log 0.5}, y_2 = \frac{\log 2}{\log 3} + x$

Question

which system of equations could be graphed to solve the equation below?

$\log_{0.5} x = \log_{3} 2 + x$

$y_1 = \frac{\log 0.5}{x}, y_2 = \frac{\log 3}{2+x}$

$y_1 = \frac{\log x}{\log 0.5}, y_2 = \frac{\log 2+x}{\log 3}$

$y_1 = \frac{\log 0.5}{\log 3}, y_2 = \frac{\log x}{\log 2+x}$

$y_1 = \frac{\log x}{\log 0.5}, y_2 = \frac{\log 2}{\log 3} + x$

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 Equations" ] } ## Split the equation into a system of two equations $$ \begin{aligned} &y_1 = \log_{0.5} x \ &y_2 = \log_{3} 2 + x \end{aligned} $$ ## Apply the change of base formula to each equation $$ \begin{aligned} &y_1 = \frac{\log x}{\log 0.5} \ &y_2 = \frac{\log 2}{\log 3} + x \end{aligned} $$

(A) $y_1 = \frac{\log 0.5}{x}, y_2 = \frac{\log 3}{2+x}$

(B) $y_1 = \frac{\log x}{\log 0.5}, y_2 = \frac{\log(2+x)}{\log 3}$

(C) $y_1 = \frac{\log 0.5}{\log 3}, y_2 = \frac{\log x}{\log(2+x)}$

(D) $y_1 = \frac{\log x}{\log 0.5}, y_2 = \frac{\log 2}{\log 3} + x$

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

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QUESTION IMAGE

Question

Explanation:

Split the equation into a system of two equations

Apply the change of base formula to each equation

Answer: