Question

expand: \\(\ln (4a)^3\\)

\\(3 \ln 4 + \ln a\\)
\\(3 \ln 4 - 3 \ln a\\)
\\(3 \ln 4 + 3 \ln a\\)

Explanation:

Apply the power rule for logarithms

Using the Logarithmic Power Rule knowledge point

$$ \ln(4a)^3 = 3 \ln(4a) $$

Apply the product rule for logarithms

Using the Logarithmic Product Rule to expand the product inside the logarithm:

$$ \ln(4a) = \ln(4) + \ln(a) $$

Distribute the coefficient

Distribute the constant factor \(3\) to each term in the sum:

$$ 3(\ln(4) + \ln(a)) = 3 \ln 4 + 3 \ln a $$

Answer:

• \(3 \ln 4 + \ln a\)
• \(3 \ln 4 - 3 \ln a\)
• \(3 \ln 4 + 3 \ln a\) (Correct answer)