expand the logarithm fully using the properties of logs. express the final answer in terms of log x, and log…
expand the logarithm fully using the properties of logs. express the final answer in terms of log x, and log y. log x⁴y⁵
Answer
Explanation:
Step1: Apply product rule of logs
The product rule of logarithms states that $\log(ab) = \log a + \log b$. So, for $\log(x^{4}y^{5})$, we can split it as $\log(x^{4}) + \log(y^{5})$.
Step2: Apply power rule of logs
The power rule of logarithms states that $\log(a^{n}) = n\log a$. Applying this to $\log(x^{4})$ and $\log(y^{5})$, we get $4\log x + 5\log y$.
Answer:
$4\log x + 5\log y$