Question

which equation is equivalent to \\(\log 4 + \log(x + 2) = 1\\)?

\\(x - 2 = 10^1\\)

\\(4x + 8 = 10^1\\)

\\(4x + 8 = 1\\)

\\(\frac{4}{x + 2} = 10^1\\)

Explanation:

Apply the product rule of logarithms

Using the Logarithmic Product Rule knowledge point

$$ \log(4) + \log(x + 2) = \log(4(x + 2)) = \log(4x + 8) $$

Rewrite in exponential form

Using the Solving Logarithmic Equations knowledge point

$$
LATEXBLOCK0
$$

Answer:

• \(x - 2 = 10^1\)
• \(4x + 8 = 10^1\) (Correct answer)
• \(4x + 8 = 1\)
• \(\frac{4}{x + 2} = 10^1\)