Question

Question was provided via image upload.

Explanation:

Apply the change of base formula

Using the Change of Base Formula knowledge point

$$ \log_{9}(5) = \frac{\log(5)}{\log(9)} $$

Define the system of equations

Using the Graphical Solution of Systems knowledge point

$$
LATEXBLOCK0
$$

Solve for the intersection point

$$
LATEXBLOCK1
$$

Select the closest approximation

Comparing the calculated value \(x \approx 2.09\) with the dropdown options:

• \(0.732\)
• \(1.36\)
• \(1.80\)
• \(2.09\)

The closest matching value is \(2.09\).

Answer:

Question 1

What equation(s) should be graphed?

• (A) \(y_1 = \frac{\log 5}{\log 9}\) (Correct answer)
• (B) \(y_1 = \frac{\log 9}{\log 5}\)
• (C) \(y_2 = 7 - 3x\) (Correct answer)
• (D) \(y_2 = -3x\)

Question 2

Graph the system. Use the graph to approximate the solution of the equation \(\log_{9}5 = 7 - 3x\).

• (A) 0.732
• (B) 1.36
• (C) 1.80
• (D) 2.09 (Correct answer)