Question

question
expand the logarithm fully using the properties of logs. express the final answer in terms of \\(\log x\\), and \\(\log y\\).
\\(\log \frac{x^5}{y^2}\\)
answer attempt 1 out of 2

Explanation:

Step1: Apply Quotient Rule of Logs

The quotient rule of logarithms states that $\log \frac{a}{b} = \log a - \log b$. For $\log \frac{x^5}{y^2}$, we apply this rule:
$\log \frac{x^5}{y^2} = \log x^5 - \log y^2$

Step2: Apply Power Rule of Logs

The power rule of logarithms states that $\log a^n = n\log a$. We apply this to both terms:
For $\log x^5$, we get $5\log x$.
For $\log y^2$, we get $2\log y$.

Step3: Combine the Results

Substituting these back into the expression from Step 1, we have:
$5\log x - 2\log y$

Answer:

$5\log x - 2\log y$