Question

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

\\(\log(2x+1) = 3x-2\\)

\\(y_1 = 3x, y_2 = 2x\\)
\\(y_1 = \log(2x+1), y_2 = 3x-2\\)
\\(y_1 = \log 2x+1, y_2 = 3x-2\\)
\\(y_1 = \log(2x+1+2), y_2 = 3x\\)

Explanation:

Identify the given equation

Using the Graphical Solution of Equations and Systems of Equations from Single Equations knowledge points

$$ \log(2x+1) = 3x-2 $$

Split the equation into a system

Using the Systems of Equations from Single Equations knowledge point

$$
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$$

Answer:

• (A) \(y_1 = 3x\), \(y_2 = 2x\)
• (B) \(y_1 = \log(2x+1)\), \(y_2 = 3x-2\) (Correct answer)
• (C) \(y_1 = \log 2x+1\), \(y_2 = 3x-2\)
• (D) \(y_1 = \log(2x+1+2)\), \(y_2 = 3x\)