Question

expanding logarithmic expressions
expand the expression.
$ln 3x = $
options:
$3 ln x$
$ln 3 - ln x$
$ln 3 + ln x$

Explanation:

Step1: Recall Logarithm Product Rule

The product rule for logarithms states that $\ln(ab) = \ln(a) + \ln(b)$ for positive real numbers $a$ and $b$.

Step2: Apply the Rule to $\ln(3x)$

Here, $a = 3$ and $b = x$. So, applying the product rule, we get $\ln(3x) = \ln(3) + \ln(x)$.

Answer:

$\ln 3 + \ln x$ (corresponding to the option "ln 3 + ln x")