Question

solve \\(\log_{2}x = \log_{12}x\\) by graphing.

what equations should be graphed?

\\(y_1 = \frac{\log 2}{\log x}\\)
\\(y_1 = \frac{\log x}{\log 2}\\)
\\(y_2 = \frac{\log x}{\log 12}\\)
\\(y_2 = \frac{\log 12}{\log x}\\)

Explanation:

Apply change of base to first term

Using the Change of Base Formula knowledge point

$$ y_1 = \log_{2}x = \frac{\log x}{\log 2} $$

Apply change of base to second term

Using the Change of Base Formula knowledge point

$$ y_2 = \log_{12}x = \frac{\log x}{\log 12} $$

Identify correct system of equations

Using the Solving Exponential Equations Graphically knowledge point

$$
LATEXBLOCK0
$$

Answer:

• \(y_1 = \frac{\log 2}{\log x}\)
• \(y_1 = \frac{\log x}{\log 2}\) (Correct answer)
• \(y_2 = \frac{\log x}{\log 12}\) (Correct answer)
• \(y_2 = \frac{\log 12}{\log x}\)