Question

which expression is equivalent to \\(\log 3 (x + 4)\\)? \\(\log 3 + \log (x + 4)\\) \\(\log 12 + \log x\\) \\(\log 3 \div \log (x + 4)\\) \\(\log 3 - \log (x + 4)\\)

Explanation:

Step1: Recall Logarithm Product Rule

The product rule of logarithms states that $\log_b(ac) = \log_b(a) + \log_b(c)$ for any positive numbers $a$, $b$ (where $b
eq1$), and $c$. If we consider the common logarithm (base 10, though the base isn't specified here but the rule holds for any valid base), and we rewrite $\log(3(x + 4))$ as a product inside the log, we can apply the product rule.

Step2: Apply the Product Rule

Using the product rule $\log(a\times b)=\log(a)+\log(b)$, where $a = 3$ and $b=(x + 4)$, we get $\log(3(x + 4))=\log(3)+\log(x + 4)$.

Answer:

$\log 3 + \log (x + 4)$