Question

question
expand the logarithm fully using the properties of logs. express the final answer in terms of \\(\log x\\), and \\(\log y\\).
\\(\log x^4 y^3\\)

Explanation:

Step1: Apply product rule of logs

The product rule of logarithms states that $\log(ab)=\log(a)+\log(b)$. For $\log(x^{4}y^{3})$, we can split it into $\log(x^{4})+\log(y^{3})$.

Step2: Apply power rule of logs

The power rule of logarithms states that $\log(a^{n}) = n\log(a)$. Applying this to $\log(x^{4})$ gives $4\log(x)$ and to $\log(y^{3})$ gives $3\log(y)$.

Answer:

$4\log x + 3\log y$