Question

use the properties of logarithms to write the expression as a sum, difference, or product of simpler logarithms. for example, \\(\log_2(\sqrt{3}x)=\frac{1}{2}\log_2 3 + \log_2 x\\). \\(\log_7(2k)\\) write the expression as a sum, difference, or product of simpler logarithms. \\(\log_7(2k)=\square\\)

Explanation:

Step1: Recall Log Product Rule

The product rule for logarithms states that $\log_b(MN) = \log_b M + \log_b N$, where $b>0, b
eq1, M>0, N>0$.

Step2: Apply the Rule to $\log_7(2k)$

Here, $b = 7$, $M = 2$, and $N = k$. Using the product rule, we can split the logarithm of the product into the sum of the logarithms: $\log_7(2k)=\log_7 2 + \log_7 k$.

Answer:

$\log_7 2 + \log_7 k$