Question

rewrite the logarithmic expression as a single lo\\(\log_{5}5 + \log_{5}3\\)

Explanation:

Step1: Recall logarithm product rule

The product rule for logarithms states that $\log_b M + \log_b N = \log_b (M \times N)$ for the same base $b$, where $M$ and $N$ are positive real numbers.

Step2: Apply the product rule

Here, $b = 5$, $M = 5$, and $N = 3$. So we apply the product rule to $\log_5 5 + \log_5 3$:
$\log_5 5 + \log_5 3 = \log_5 (5 \times 3)$

Step3: Simplify the argument

Calculate $5 \times 3 = 15$. So the expression becomes $\log_5 15$.

Answer:

$\log_5 15$