Question

question
expand the logarithm fully using the properties of logs. express the final answer in terms of \\(\log x\\).
\\(\log 8x^5\\)
\\(\boxed{}\\)

Explanation:

Step1: Apply product rule of logs

The product rule of logarithms states that $\log(ab) = \log a + \log b$. For $\log(8x^5)$, we can split it as $\log 8 + \log x^5$.

Step2: Apply power rule of logs

The power rule of logarithms states that $\log a^n = n\log a$. For $\log x^5$, we apply the power rule to get $5\log x$. So the expanded form is $\log 8 + 5\log x$.

Answer:

$\log 8 + 5\log x$