Question

expand each expression.

\\(\ln 3x = \\)

options:

• \\(3 \ln x\\)
• \\(\ln 3 - \ln x\\)
• \\(\ln 3 + \ln x\\)

Explanation:

⚡ Using what you learned: properties of logarithms

Step 1: Identify the product inside the logarithm

The given expression is:

$$ \ln(3x) $$

The argument of the natural logarithm is the product of \( 3 \) and \( x \).

Step 2: Apply the product property of logarithms

The product property states:

$$ \log_b(M \cdot N) = \log_b(M) + \log_b(N) $$

Applying this to the natural logarithm:

$$ \ln(3 \cdot x) = \ln(3) + \ln(x) $$

Answer:

$$ \ln 3 + \ln x $$