Question

kim solved the equation below by graphing a system of equations.

\\(\log_{2}(3x-1) = \log_{4}(x+8)\\)

what is the approximate solution to the equation?

• 0.6
• 0.9
• 1.4
• 1.6

Explanation:

Apply change of base formula

Using the Change of Base Formula knowledge point

$$ \log_4(x+8) = \frac{\log_2(x+8)}{\log_2(4)} = \frac{\log_2(x+8)}{2} $$

Rewrite the equation

Using the Solving Logarithmic Equations knowledge point

$$
LATEXBLOCK0
$$

Solve the quadratic equation

Using the Solving Logarithmic Equations knowledge point

$$
LATEXBLOCK1
$$

Apply the quadratic formula

Using the Solving Logarithmic Equations knowledge point

$$
LATEXBLOCK2
$$

Evaluate and check domain

Using the Solving Logarithmic Equations knowledge point

$$
LATEXBLOCK3
$$

Answer:

• (A) 0.6
• (B) 0.9
• (C) 1.4 (Correct answer)
• (D) 1.6