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?

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

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

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

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

Explanation:

Set up the system of equations

Using the Solving Exponential Equations Graphically knowledge point

$$
LATEXBLOCK0
$$

Apply change of base formula

Using the Change of Base Formula knowledge point

$$
LATEXBLOCK1
$$

Answer:

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